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Journal articles on the topic 'Distributions'

Author: Grafiati

Published: 4 June 2021

Last updated: 15 June 2025

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1

Omer, Abdeen. "Medicines Distribution, Regulatory Privatisation, Social Welfare Services and Financing Alternatives." International Journal of Medical Reviews and Case Reports 2, Reports in Surgery and Dermatolo (2018): 1. http://dx.doi.org/10.5455/ijmrcr.medicine-distributions-sudan.

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Abdeen, Omer, Amiry Sabrina, and Inkov Ivan. "Medicines Distribution, Regulatory Privatisation, Social Welfare Services and Financing Alternatives." International Journal of Medical Reviews and Case Reports 3, no. 1 (2018): 16–34. https://doi.org/10.5455/IJMRCR.medicine-distributions-sudan.

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The strategy of price liberalisation and privatisation had been implemented in Sudan over the last decade, and has had a positive result on government deficit. The investment law approved recently has good statements and rules on the above strategy in particular to pharmacy regulations. Under the pressure of the new privatisation policy, the government introduced radical changes in the pharmacy regulations. To improve the effectiveness of the public pharmacy, resources should be switched towards areas of need, reducing inequalities and promoting better health conditions. Medicines are financed either through cost sharing or full private. The role of the private services is significant. A review of reform of financing medicines in Sudan is given in this study. Also, it highlights the current drug supply system in the public sector, which is currently responsibility of the Central Medical Supplies Public Corporation (CMS). In Sudan, the researchers did not identify any rigorous evaluations or quantitative studies about the impact of drug regulations on the quality of medicines and how to protect public health against counterfeit or low quality medicines, although it is practically possible. However, the regulations must be continually evaluated to ensure the public health is protected against by marketing high quality medicines rather than commercial interests, and the drug companies are held accountable for their conduct.

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C, Roshni, Venkatesan D, and B. Prasanth C. "A Generalized Area-Biased Power Ishita Distribution - Properties and Applications." Indian Journal of Science and Technology 17, no. 29 (2024): 3037–43. https://doi.org/10.17485/IJST/v17i29.1515.

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Abstract <strong>Objectives:</strong> Generalized Area-Biased Power Ishita Distribution (GAPID) is a brand-new distribution that was suggested in this study. Its characterization is also mentioned in detail. <strong>Methods:</strong> The idea of weighted distributions is incorporated. This helps to derive new distributions that will be a best fit for many real-life data from many domains like agriculture, biomedical, financial, etc., where they may not match with the conventional distributions. Thus, it becomes necessary to create new distributions. The parameters have been calculated by maximum likelihood estimation. <strong>Findings:</strong> Its hazard rate function, survival function, and Moments, among other statistical features, were explored. <strong>Novelty:</strong> As results from classical distributions are insufficient for many Biomedical datasets, this novel distribution was fitted to a real data set of lung cancer patients' survival periods in months, allowing for a discussion of the data set's use. The superiority of the distribution is tested by comparing the same with known distributions and finding this one is better. Thereby the importance of the said distribution is established. <strong>Keywords:</strong> Estimate, Weighted distributions, Parameters, Reliability, Ishita distribution

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Sulewski, Piotr, and Marcin Szymkowiak. "Modelling income distributions based on theoretical distributions derived from normal distributions." Wiadomości Statystyczne. The Polish Statistician 2023, no. 6 (2023): 1–23. http://dx.doi.org/10.59139/ws.2023.06.1.

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In income modelling studies, such well-known distributions as the Dagum, the lognormal or the Zenga distributions are often used as approximations of the observed distributions. The objective of the research described in the article is to verify the possibility of using other type of distributions, i.e. asymmetric distributions derived from normal distribution (ND) in the context of income modelling. Data from the 2011 EU-SILC survey on the monthly gross income per capita in Poland were used to assess the most important characteristics of the discussed distributions. The probability distributions were divided into two groups: I – distributions commonly used for income modelling (e.g. the Dagum distribution) and II – distributions derived from ND (e.g. the SU Johnson distribution). In addition to the visual evaluation of the usefulness of the analysed probability distributions, various numerical criteria were applied: information criteria for econometric models (such as the Akaike Information Criterion, Schwarz’s Bayesian Information Criterion and the Hannan-Quinn Information Criterion), measures of agreement, as well as empirical and theoretical characteristics, including a measure based on quantiles, specifically defined by the authors for the purposes of this article. The research found that the SU Johnson distribution (Group II), similarly to the Dagum distribution (Group I), can be successfully used for income modelling.

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Panton, Don B. "Distribution function values for logstable distributions." Computers & Mathematics with Applications 25, no. 9 (1993): 17–24. http://dx.doi.org/10.1016/0898-1221(93)90128-i.

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Marengo, James E., David L. Farnsworth, and Lucas Stefanic. "A Geometric Derivation of the Irwin-Hall Distribution." International Journal of Mathematics and Mathematical Sciences 2017 (2017): 1–6. http://dx.doi.org/10.1155/2017/3571419.

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The Irwin-Hall distribution is the distribution of the sum of a finite number of independent identically distributed uniform random variables on the unit interval. Many applications arise since round-off errors have a transformed Irwin-Hall distribution and the distribution supplies spline approximations to normal distributions. We review some of the distribution’s history. The present derivation is very transparent, since it is geometric and explicitly uses the inclusion-exclusion principle. In certain special cases, the derivation can be extended to linear combinations of independent uniform random variables on other intervals of finite length. The derivation adds to the literature about methodologies for finding distributions of sums of random variables, especially distributions that have domains with boundaries so that the inclusion-exclusion principle might be employed.

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TRANDAFIR, Romică, Vasile PREDA, Sorin DEMETRIU, and Ion MIERLUŞ-MAZILU. "ON MIXING CONTINUOUS DISTRIBUTIONS WITH DISCRETE DISTRIBUTIONS USED IN RELIABILITY." Review of the Air Force Academy 16, no. 2 (2018): 5–16. http://dx.doi.org/10.19062/1842-9238.2018.16.2.1.

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Aguirre, M. A., and C. K. Li. "The distributional products of particular distributions." Applied Mathematics and Computation 187, no. 1 (2007): 20–26. http://dx.doi.org/10.1016/j.amc.2006.08.098.

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9

Clancy, Damian, and Philip K. Pollett. "A note on quasi-stationary distributions of birth–death processes and the SIS logistic epidemic." Journal of Applied Probability 40, no. 03 (2003): 821–25. http://dx.doi.org/10.1017/s002190020001977x.

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For Markov processes on the positive integers with the origin as an absorbing state, Ferrari, Kesten, Martínez and Picco studied the existence of quasi-stationary and limiting conditional distributions by characterizing quasi-stationary distributions as fixed points of a transformation Φ on the space of probability distributions on {1, 2, …}. In the case of a birth–death process, the components of Φ(ν) can be written down explicitly for any given distributionν. Using this explicit representation, we will show that Φ preserves likelihood ratio ordering between distributions. A conjecture of Kryscio and Lefèvre concerning the quasi-stationary distribution of the SIS logistic epidemic follows as a corollary.

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Chaudhary, Arun Kumar, Lal Babu Sah Telee, and Vijay Kumar. "Modified Half -Cauchy Chen (MHCC) Distribution with Applications to Lifetime Dataset." NCC Journal 9, no. 1 (2024): 112–20. https://doi.org/10.3126/nccj.v9i1.72259.

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In this article, we have recommended an innovative versatile distribution called Modified Half-Cauchy Chen distribution by modifying half-Cauchy Chen distribution. The recommended distribution's various properties are derived and analyzed. The recommended distribution's parameters are ascertained by applying the maximum likelihood estimation (MLE) approach. Furthermore, the performance of the Modified Half-Cauchy Chen distribution is compared against other distributions using various statistical measures. These measures consist of the Corrected Akaike Information Criterion (CAIC), the Kolmogorov-Smirnov (K-S) test, the Bayesian Information Criterion (BIC), and the Akaike Information Criterion (AIC). The results consistently demonstrate the superior fit of the Modified Half-Cauchy Chen distribution to the data. The goodness-of-fit analysis is carried out on a real data set in order to evaluate the innovative distribution's applicability. The Modified half-Cauchy Chen distribution is shown to perform better than a few other known distributions. R programming software is used to help with every computation.

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Agboola, Sunday Olanrewaju, Abayomi Ayoade, Dekera Washachi, and Mohammed Abdullahi. "The Analysis of Hypo-Exponential and Hyper-Exponential Distributions in Solving Performance Measures for General Phase Type Distributions." International Journal of Development Mathematics (IJDM) 1, no. 4 (2024): 177–90. https://doi.org/10.62054/ijdm/0104.13.

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The importance of phase-type distribution in modeling activities cannot be under emphasized when both a distribution's initial and second moments are accessible, or when the sequence of data points for computing moments is the information available. In continuous time process for an absorbing finite state Markov chain, the phase-type distribution can be thought of as the of the time until absorption, and it is widely used in queueing theories and other fields of applied probabilities. The common phase-type distributions are generalized Erlang, Coxian, Hypo-exponential, and Hyper-exponential distributions. In this study, performance measures of phase-type distribution using Hypo-exponential, and Hyper-exponential distributions have been looked into, in order to provide meaningful study into the probability function, mean, moment, variance, Laplace Stieltjes transform and squared coefficient of variation of phase type distribution. The study started by considering the tractability and memory less properties of exponential distribution, and since these properties are not enough, we examined the journey through a series of exponential phases to arrive at performance measures. Illustrative examples are demonstrated for various cases to arrive at various values for probability functions, Laplace Stieltjes transform, squared coefficient of variation, moment, mean and variance for the phase type distribution.

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Warsono and Dian Kurniasari. "On the Characteristic Function of the Four-Parameter Generalized Beta of the Second Kind (GB2) Distribution and Its Approximation to the Singh-Maddala, Dagum, and Fisk Distributions." Science and Technology Indonesia 10, no. 1 (2025): 201–11. https://doi.org/10.26554/sti.2025.10.1.201-211.

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Researchers have thoroughly investigated generalized distributions due to their inherent flexibility, which allows them to include several well-known distributions as special cases. Among these, the four parameter Generalized Beta of the Second Kind (GB2) distribution stands out as one of the most versatile frameworks in probability theory. Despite its broad applications, the GB2 distribution’s characteristic function, a critical tool in probability and statistical analysis, lacks a closed-form solution in the existing literature. This study pursues two primary objectives: first, to derive the characteristic function and the kth moment of the GB2 distribution, and second, to demonstrate how the GB2 distribution can serve as a close approximation to the Singh-Maddala, Dagum, and Fisk distributions using its characteristic function and kth moment. These derivations and approximations rely on gamma and beta functions, supplemented by the Maclaurin series expansion.

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Cousineau, Denis, Jean-Philippe Thivierge, Bradley Harding, and Yves Lacouture. "Constructing a group distribution from individual distributions." Canadian Journal of Experimental Psychology/Revue canadienne de psychologie expérimentale 70, no. 3 (2016): 253–77. http://dx.doi.org/10.1037/cep0000069.

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Moya-Cessa, J. R., H. Moya-Cessa, L. R. Berriel-Valdos, O. Aguilar-Loreto, and P. Barberis-Blostein. "Unifying distribution functions: some lesser known distributions." Applied Optics 47, no. 22 (2008): E13. http://dx.doi.org/10.1364/ao.47.000e13.

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Deshmukh, S. R., and M. S. Kasture. "BIVARIATE DISTRIBUTION WITH TRUNCATED POISSON MARGINAL DISTRIBUTIONS." Communications in Statistics - Theory and Methods 31, no. 4 (2002): 527–34. http://dx.doi.org/10.1081/sta-120003132.

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Li, Kaican, and Zhi Geng. "The Noncentral Wishart Distribution and Related Distributions." Communications in Statistics - Theory and Methods 32, no. 1 (2003): 33–45. http://dx.doi.org/10.1081/sta-120017798.

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Castillo, E., and J. Galambos. "Conditional distributions and the bivariate normal distribution." Metrika 36, no. 1 (1989): 209–14. http://dx.doi.org/10.1007/bf02614094.

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Voit, Eberhard O., and Shuiyang Yu. "The S-Distribution: Approximation of Discrete Distributions." Biometrical Journal 36, no. 2 (1994): 205–19. http://dx.doi.org/10.1002/bimj.4710360215.

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Suleiman, Ahmad Abubakar, Hanita Daud, Narinderjit Singh Sawaran Singh, Mahmod Othman, Aliyu Ismail Ishaq, and Rajalingam Sokkalingam. "A Novel Odd Beta Prime-Logistic Distribution: Desirable Mathematical Properties and Applications to Engineering and Environmental Data." Sustainability 15, no. 13 (2023): 10239. http://dx.doi.org/10.3390/su151310239.

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In parametric statistical modeling, it is important to construct new extensions of existing probability distributions (PDs) that can make modeling data more flexible and help stakeholders make better decisions. In the present study, a new family of probability distributions (FPDs) called the odd beta prime generalized (OBP-G) FPDs is proposed to improve the traditional PDs. A new PD called the odd beta prime-logistic (OBP-logistic) distribution has been developed based on the developed OBP-G FPDs. Some desirable mathematical properties of the proposed OBP-logistic distribution, including the moments, moment-generating function, information-generating function, quantile function, stress–strength, order statistics, and entropies, are studied and derived. The proposed OBP-logistic distribution’s parameters are determined by adopting the maximum likelihood estimation (MLE) method. The applicability of the new PD was demonstrated by employing three data sets and these were compared by the known extended logistic distributions, such as the gamma generalized logistic distribution, new modified exponential logistic distribution, gamma-logistic distribution, exponential modified Weibull logistic distribution, exponentiated Weibull logistic distribution, and transmuted Weibull logistic distribution. The findings reveal that the studied distribution provides better results than the competing PDs. The empirical results showed that the new OBP-logistic distribution performs better than the other PDs based on several statistical metrics. We hoped that the newly constructed OBP-logistic distribution would be an alternative to other well-known extended logistic distributions for the statistical modeling of symmetric and skewed data sets.

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Alhaji Modu Isa, Sule Omeiza Bashiru, Alhaji Buhari Ali, Akeem Ajibola Adepoju, and Ibrahim Ismaila Itopa. "Sine-Exponential Distribution: Its Mathematical Properties and Application to Real Dataset." UMYU Scientifica 1, no. 1 (2022): 127–31. http://dx.doi.org/10.56919/usci.1122.017.

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To increase flexibility or to develop covariate models in various ways, new parameters can be added to existing families of distributions or a new family of distributions can be compounded with well-known standard normal distribution. In this paper, a trigonometric-type distribution was developed in order to come up with flexible distribution without adding parameters, considering Exponential distribution as the baseline distribution and Sine-G as the generator. The proposed distribution is referred to as Sine Exponential Distribution. Statistical features, including the moment, moment generating function, entropy, and order statistics were obtained. The proposed distribution's parameters were estimated using the Maximum Likelihood method. Using real datasets, the model's importance was demonstrated. The newly developed model was proven to be better than its competitors.

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Alsolami, Eatemad, and Dawlah Alsulami. "Combining Two Exponentiated Families to Generate a New Family of Distributions." Symmetry 14, no. 8 (2022): 1739. http://dx.doi.org/10.3390/sym14081739.

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This article presents a new technique to generate distributions that have the ability to fit any complex data called the exponentiated exponentiated Weibull-X (EEW-X) family, and the exponentiated exponentiated Weibull exponential (EEWE) distribution is presented as a member of this family. The new distribution’s unknown parameters were calculated by applying the maximum likelihood method. Some statistical properties, such as quantile, Rényi entropy, order statistics, and median are obtained for the proposed distribution. A simulation study was performed for different cases to investigate the estimation method’s performance. Three real datasets have been applied in which the new distribution has shown more flexibility compared to some other distributions.

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Adisa, Agbona Anthony, Odukoya Elijah Ayooluwa, Amalare Asimi, and Ayeni Taiwo Michael. "Exponential-Gamma-Rayleigh Distribution: Theory and Properties." Asian Journal of Probability and Statistics 27, no. 3 (2025): 134–44. https://doi.org/10.9734/ajpas/2025/v27i3730.

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The use of traditional probability models to forecast real-world events is causing growing dissatisfaction among scholars. One of the motives could be the tail characteristics and goodness of fit metrics has a constraining tendency. Subsequently, there has been a significant increase in the generalisation of well-known probability distributions in recent years. The challenge is finding families versatile enough to fit both skewed and symmetric data. It is essential to understand that most generalised distributions described in the literature were developed using the generalised transformed transformer (T-X) method. This method was proposed by Alzaatreh et al. (2013). Also, Adewusi et al. (2019) showed that this generalization approach is beneficial by transforming the Exponential-Gamma distribution developed by Ogunwale et al. (2019) to a family of distribution known as the Exponential-Gamma-X. Therefore, in this study, we focused on developing a new family of continuous distributions called the Exponential-Gamma-Rayleigh distribution by transforming the newly generated continuous T-X family of distribution called the Exponential-Gamma-X distribution using the traditionally existing Rayleigh distribution as a transformer “X”. Several expressions for the new distribution’s theory and properties were explored and obtained; the maximum likelihood estimation approach was used to estimate the distributions' parameters, and finally, simulations studies were conducted to assess the asymptotic behaviour of the estimates.

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Kabir, Umar, and Terna Godfrey IEREN. "On the inferences and applications of transmuted exponential Lomax distribution." International Journal of Advanced Statistics and Probability 6, no. 1 (2018): 30. http://dx.doi.org/10.14419/ijasp.v6i1.8129.

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This article proposed a new distribution referred to as the transmuted Exponential Lomax distribution as an extension of the popular Lomax distribution in the form of Exponential Lomax by using the Quadratic rank transmutation map proposed and studied in earlier research. Using the transmutation map, we defined the probability density function (PDF) and cumulative distribution function (CDF) of the transmuted Exponential Lomax distribution. Some properties of the new distribution were extensively studied after derivation. The estimation of the distribution’s parameters was also done using the method of maximum likelihood estimation. The performance of the proposed probability distribution was checked in comparison with some other generalizations of Lomax distribution using three real-life data sets. The results obtained indicated that TELD performs better than the other distributions comprising power Lomax, Exponential-Lomax, and the Lomax distributions.

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Ejsmont, Wiktor. "Free Meixner Distributions." Didactics of Mathematics 13, no. 17 (2016): 13–16. http://dx.doi.org/10.15611/dm.2016.13.02.

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Lindenberg, Björn, Jonas Nordqvist, and Karl-Olof Lindahl. "Conjugated Discrete Distributions for Distributional Reinforcement Learning." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 7 (2022): 7516–24. http://dx.doi.org/10.1609/aaai.v36i7.20716.

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In this work we continue to build upon recent advances in reinforcement learning for finite Markov processes. A common approach among previous existing algorithms, both single-actor and distributed, is to either clip rewards or to apply a transformation method on Q-functions to handle a large variety of magnitudes in real discounted returns. We theoretically show that one of the most successful methods may not yield an optimal policy if we have a non-deterministic process. As a solution, we argue that distributional reinforcement learning lends itself to remedy this situation completely. By the introduction of a conjugated distributional operator we may handle a large class of transformations for real returns with guaranteed theoretical convergence. We propose an approximating single-actor algorithm based on this operator that trains agents directly on unaltered rewards using a proper distributional metric given by the Cramér distance. To evaluate its performance in a stochastic setting we train agents on a suite of 55 Atari 2600 games using sticky-actions and obtain state-of-the-art performance compared to other well-known algorithms in the Dopamine framework.

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Hossein, Iravani, and Yari Gholamhossein. "GENERALIZATION OF BURR DISTRIBUTION AND INTRODUCTION OF A NEW FAMILY OF STATISTICAL DISTRIBUTIONS." Matrix Science Mathematic 8, no. 2 (2024): 31–37. https://doi.org/10.26480/msmk.02.2024.31.37.

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The family of Burr distributions consists of twelve different distributions that result from solving a differential equation. This family is part of the family of continuous distributions and its applications have been investigated in various topics such as survival function, simulation problems, and economic and insurance analyses. Since the flexibility of the generalized distributions is often greater than the distribution itself, the generalization of the distributions of this family is of great interest. Also, due to the diversity of the distribution type, various generalizations of the Burr distribution have been presented. Regarding the importance of generalized distributions in this family, it is enough that the family of Burr distributions can be considered a parametric generalized family. In this article, it is intended to present a generalization of the Burr distribution, which results in the special case of the type II Burr distribution; In this way, we add a parameter in the type II Burr distribution structure and by changing this parameter, we reach different Burr distributions, including the type II Burr distribution. The mentioned parameter along with other distribution parameters is estimated by the maximum likelihood method.

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Papalexiou, S. M., D. Koutsoyiannis, and C. Makropoulos. "How extreme is extreme? An assessment of daily rainfall distribution tails." Hydrology and Earth System Sciences Discussions 9, no. 5 (2012): 5757–78. http://dx.doi.org/10.5194/hessd-9-5757-2012.

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Abstract. The upper part of a probability distribution, usually known as the tail, governs both the magnitude and the frequency of extreme events. The tail behaviour of all probability distributions may be, loosely speaking, categorized in two families: heavy-tailed and light-tailed distributions, with the latter generating more "mild" and infrequent extremes compared to the former. This emphasizes how important for hydrological design is to assess correctly the tail behaviour. Traditionally, the wet-day daily rainfall has been described by light-tailed distributions like the Gamma, although heavier-tailed distributions have also been proposed and used, e.g. the Lognormal, the Pareto, the Kappa, and others. Here, we investigate the issue of tails for daily rainfall by comparing the upper part of empirical distributions of thousands of records with four common theoretical tails: those of the Pareto, Lognormal, Weibull and Gamma distributions. Specifically, we use 15 029 daily rainfall records from around the world with record lengths from 50 to 163 yr. The analysis shows that heavier-tailed distributions are in better agreement with the observed rainfall extremes than the more often used lighter tailed distributios, with clear implications on extreme event modelling and engineering design.

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Tamraz, Maissa, and Raluca Vernic. "ON THE EVALUATION OF MULTIVARIATE COMPOUND DISTRIBUTIONS WITH CONTINUOUS SEVERITY DISTRIBUTIONS AND SARMANOV'S COUNTING DISTRIBUTION." ASTIN Bulletin 48, no. 02 (2018): 841–70. http://dx.doi.org/10.1017/asb.2017.46.

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AbstractIn this paper, we present closed-type formulas for some multivariate compound distributions with multivariate Sarmanov counting distribution and independent Erlang distributed claim sizes. Further on, we also consider a type-II Pareto dependency between the claim sizes of a certain type. The resulting densities rely on the special hypergeometric function, which has the advantage of being implemented in the usual software. We numerically illustrate the applicability and efficiency of such formulas by evaluating a bivariate cumulative distribution function, which is also compared with the similar function obtained by the classical recursion-discretization approach.

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Withers, Christopher S., and Saralees Nadarajah. "The distribution and quantiles of functionals of weighted empirical distributions when observations have different distributions." Statistics & Probability Letters 80, no. 13-14 (2010): 1093–102. http://dx.doi.org/10.1016/j.spl.2010.03.003.

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Alsulami, Eftekhar, Lutfiah Al-Turk, and Muhammad Shahbaz. "A New Method of Generating Truncated Bivariate Families of Distributions." European Journal of Pure and Applied Mathematics 17, no. 4 (2024): 3945–72. http://dx.doi.org/10.29020/nybg.ejpam.v17i4.5507.

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The modeling of complex data has attracted several researchers for the quest of generating new probability distributions. The joint modeling of two variables asks for some additional complexities as a bivariate distribution is needed. The field of research in developing bivariate families of distributions is somewhat new. In certain situations, the domain of data is restricted and some truncated distribution is required. Several univariate truncated families of distributions are available for modeling of a single variable but the bivariate truncated families of distributions has not been studied and in this paper, we have proposed a new bivariate truncated families of distributions. A specific sub-family has been proposed by using the bivariate Burr as a base-line distribution, resulting in a bivariate truncated Burr family of distributions. Some important statistical properties of the proposed family has been studied, which include the marginal and conditional distributions, bivariate reliability, and bivariate hazard rate functions. The maximum likelihood estimation for the parameters of the family is also carried out. The proposed bivariate truncated Burr family of distributions is studied for the Burr baseline distributions, giving rise to the bivariate truncated Burr-Burr distribution. The new bivariate truncated Burr-Burr distribution is explored in detail and several statistical properties of the new distribution are studied, which include the marginal and conditional distributions, product, ratio, and conditional moments. The maximum likelihood estimation for the parameters of the proposed distribution is done. The proposed bivariate truncated Burr-Burr distribution is used to model some real data sets. It is found that the proposed distribution performs better than the other distributions considered in this study.

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Mukherjee, Asmita, Sreeraj Nair, and Vikash Kumar Ojha. "Wigner Distributions of Quark." International Journal of Modern Physics: Conference Series 40 (January 2016): 1660055. http://dx.doi.org/10.1142/s2010194516600557.

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Wigner distribution functions are the quantum analogue of the classical phase space distribution and being quantum implies that they are not genuine phase space distribution and thus lack any probabilistic interpretation. Nevertheless, Wigner distributions are still interesting since they can be related to both generalized parton distributions (GPDs) and transverse momentum dependent parton distributions (TMDs) under some limit. We study the Wigner distribution of quarks and also the orbital angular momentum (OAM) of quarks in the dressed quark model.

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Abu El Azm, Wael S., Ehab M. Almetwally, Sundus Naji AL-Aziz, Abd Al-Aziz H. El-Bagoury, Randa Alharbi, and O. E. Abo-Kasem. "A New Transmuted Generalized Lomax Distribution: Properties and Applications to COVID-19 Data." Computational Intelligence and Neuroscience 2021 (October 7, 2021): 1–14. http://dx.doi.org/10.1155/2021/5918511.

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A new five-parameter transmuted generalization of the Lomax distribution (TGL) is introduced in this study which is more flexible than current distributions and has become the latest distribution theory trend. Transmuted generalization of Lomax distribution is the name given to the new model. This model includes some previously unknown distributions. The proposed distribution's structural features, closed forms for an rth moment and incomplete moments, quantile, and Rényi entropy, among other things, are deduced. Maximum likelihood estimate based on complete and Type-II censored data is used to derive the new distribution's parameter estimators. The percentile bootstrap and bootstrap-t confidence intervals for unknown parameters are introduced. Monte Carlo simulation research is discussed in order to estimate the characteristics of the proposed distribution using point and interval estimation. Other competitive models are compared to a novel TGL. The utility of the new model is demonstrated using two COVID-19 real-world data sets from France and the United Kingdom.

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Mačutek, Ján, Gejza Wimmer, and Michaela Koščová. "On a Parametrization of Partial-Sums Discrete Probability Distributions." Mathematics 10, no. 14 (2022): 2476. http://dx.doi.org/10.3390/math10142476.

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For every discrete probability distribution, there is one and only one partial summation which leaves the distribution unchanged. This invariance property is reconsidered for distributions with one parameter. We show that if we change the parameter value in the function which defines the summation, two families of distributions can be observed. The first of them consists of distributions which are resistant to the change. For these distributions, the change of the parameter is reversed by the normalization constant, and the distributions remain unchanged. The other contains distributions sensitive to the change. Partial summations with the changed parameter value applied to sensitive distributions result in new distributions with two parameters. A necessary and sufficient condition for a distribution to be resistant to the parameter change is presented.

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Gupta, Arjun K., and Saralees Nadarajah. "Beta Bessel distributions." International Journal of Mathematics and Mathematical Sciences 2006 (2006): 1–14. http://dx.doi.org/10.1155/ijmms/2006/16156.

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Three new distributions on the unit interval[0,1]are introduced which generalize the standard beta distribution. These distributions involve the Bessel function. Expression is derived for their shapes, particular cases, and thenth moments. Estimation by the method of maximum likelihood and Bayes estimation are discussed. Finally, an application to consumer price indices is illustrated to show that the proposed distributions are better models to economic data than one based on the standard beta distribution.

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35

Korolev, Victor. "Analytic and Asymptotic Properties of the Generalized Student and Generalized Lomax Distributions." Mathematics 11, no. 13 (2023): 2890. http://dx.doi.org/10.3390/math11132890.

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Analytic and asymptotic properties of the generalized Student and generalized Lomax distributions are discussed, with the main focus on the representation of these distributions as scale mixtures of the laws that appear as limit distributions in classical limit theorems of probability theory, such as the normal, folded normal, exponential, Weibull, and Fréchet distributions. These representations result in the possibility of proving some limit theorems for statistics constructed from samples with random sizes in which the generalized Student and generalized Lomax distributions are limit laws. An overview of known properties of the generalized Student distribution is given, and some simple bounds for its tail probabilities are presented. An analog of the ‘multiplication theorem’ is proved, and the identifiability of scale mixtures of generalized Student distributions is considered. The normal scale mixture representation for the generalized Student distribution is discussed, and the properties of the mixing distribution in this representation are studied. Some simple general inequalities are proved that relate the tails of the scale mixture with that of the mixing distribution. It is proved that for some values of the parameters, the generalized Student distribution is infinitely divisible and admits a representation as a scale mixture of Laplace distributions. Necessary and sufficient conditions are presented that provide the convergence of the distributions of sums of a random number of independent random variables with finite variances and other statistics constructed from samples with random sizes to the generalized Student distribution. As an example, the convergence of the distributions of sample quantiles in samples with random sizes is considered. The generalized Lomax distribution is defined as the distribution of the absolute value of the random variable with the generalized Student distribution. It is shown that the generalized Lomax distribution can be represented as a scale mixture of folded normal distributions. The convergence of the distributions of maximum and minimum random sums to the generalized Lomax distribution is considered. It is demonstrated that the generalized Lomax distribution can be represented as a scale mixture of Weibull distributions or that of Fréchet distributions. As a consequence, it is demonstrated that the generalized Lomax distribution can be limiting for extreme statistics in samples with random size. The convergence of the distributions of mixed geometric random sums to the generalized Lomax distribution is considered, and the corresponding extension of the famous Rényi theorem is proved. The law of large numbers for mixed Poisson random sums is presented, in which the limit random variable has a generalized Lomax distribution.

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36

Lingappaiah, Giri S. "Generalized length biased distributions." Applications of Mathematics 33, no. 5 (1988): 354–61. http://dx.doi.org/10.21136/am.1988.104316.

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Kucera, Jan, and Carlos Bosch. "Multipliers of temperate distributions." Mathematica Bohemica 130, no. 3 (2005): 225–29. http://dx.doi.org/10.21136/mb.2005.134095.

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38

Darwish, Jumanah Ahmed, Saman Hanif Shahbaz, Lutfiah Ismail Al-Turk, and Muhammad Qaiser Shahbaz. "Some bivariate and multivariate families of distributions: Theory, inference and application." AIMS Mathematics 7, no. 8 (2022): 15584–611. http://dx.doi.org/10.3934/math.2022854.

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<abstract> <p>The bivariate and multivariate probability distributions are useful in joint modeling of several random variables. The development of bivariate and multivariate distributions is relatively tedious as compared with the development of univariate distributions. In this paper we have proposed a new method of developing bivariate and multivariate families of distributions from the univariate marginals. The properties of the proposed families of distributions have been studies. These properties include marginal and conditional distributions; product, ratio and conditional moments; joint reliability function and dependence measures. Statistical inference about the proposed families of distributions has also been done. The proposed bivariate family of distributions has been studied for Weibull baseline distribution giving rise to a new bivariate Weibull distribution. The properties of the proposed bivariate Weibull distribution have been studied alongside maximum likelihood estimation of the unknown parameters. The proposed bivariate Weibull distribution has been used for modeling of real bivariate data sets and we have found that the proposed bivariate Weibull distribution has been a suitable choice for the modeling of data used.</p> </abstract>

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39

Sarabia, José María, Vanesa Jordá, Faustino Prieto, and Montserrat Guillén. "Multivariate Classes of GB2 Distributions with Applications." Mathematics 9, no. 1 (2020): 72. http://dx.doi.org/10.3390/math9010072.

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The general beta of the second kind distribution (GB2) is a flexible distribution which includes several relevant parametric families of distributions. This distribution has important applications in earnings and income distributions, finance and insurance. In this paper, several multivariate classes of the GB2 distribution are proposed. The different multivariate versions are based on two simple univariate representations of the GB2 distribution. The first type of multivariate distributions are constructed from a stochastic dependent representations defined in terms of gamma random variables. Using this representation and beginning by two particular multivariate GB2 distributions, multivariate Singh–Maddala and Dagum income distributions are presented and several properties are obtained. Then, a general multivariate GB2 distribution is introduced. The second type of multivariate distributions are based on a generalization of the distribution of the order statistics, which gives place to multivariate GB2 distribution with support above the diagonal. We discuss the role of these families in modeling bivariate income distributions. Finally, an empirical application is given, where we show that a multivariate GB2 distribution can be useful for modeling compound precipitation and wind events in the whole range.

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40

So, Jacky C. "The Distribution of Financial Ratios—A Note." Journal of Accounting, Auditing & Finance 9, no. 2 (1994): 215–23. http://dx.doi.org/10.1177/0148558x9400900205.

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Three competitive distributions are offered by the literature to explain the non-normality and skewness of the cross-sectional distribution of financial ratios: the mixture of normal distributions, the lognormal distribution, and the gamma distribution. Using a new technique, this paper shows that the lognormal distribution and the gamma distribution are not supported by the empirical evidence. Although these two distributions indeed capture skewness, they do not portray the correct shape of the distributions. The non-normal stable Paretian distribution seems to be good candidate to describe the distribution of financial ratios.

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Ch, V. Sastry. "Marshall-Olkin Stereographic Circular Logistic Distribution." YMER Digital 21, no. 06 (2022): 664–68. http://dx.doi.org/10.37896/ymer21.06/66.

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Marshall and Olkin (1997) proposed an interesting method of adding a new parameter to the existing distributions. The resulting distributions are called the MarshallOlkin distributions, these distributions include the original distributions as a special case and are more flexible and represent a wide range of behavior than the original distributions. In this paper, a new class of asymmetric stereographic circular logistic distribution is introduced by using Marshall-Olkin transformation on stereographic circular logistic distribution (Dattatreyarao et al (2016)), named as Marshall-Olkin Stereographic Circular Logistic Distribution. The proposed model admits closed form density and distribution functions, generalizes the stereographic circular logistic model and is more flexible to model various types of data (symmetric and skew-symmetric circular data). Keywords:Characteristics, Stereographic circular logistic distribution, circular data, Marshall-Olkin transformation, l -axial data.

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42

Khokhlov, Yury, Victor Korolev, and Alexander Zeifman. "Multivariate Scale-Mixed Stable Distributions and Related Limit Theorems." Mathematics 8, no. 5 (2020): 749. http://dx.doi.org/10.3390/math8050749.

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In the paper, multivariate probability distributions are considered that are representable as scale mixtures of multivariate stable distributions. Multivariate analogs of the Mittag–Leffler distribution are introduced. Some properties of these distributions are discussed. The main focus is on the representations of the corresponding random vectors as products of independent random variables and vectors. In these products, relations are traced of the distributions of the involved terms with popular probability distributions. As examples of distributions of the class of scale mixtures of multivariate stable distributions, multivariate generalized Linnik distributions and multivariate generalized Mittag–Leffler distributions are considered in detail. Their relations with multivariate ‘ordinary’ Linnik distributions, multivariate normal, stable and Laplace laws as well as with univariate Mittag–Leffler and generalized Mittag–Leffler distributions are discussed. Limit theorems are proved presenting necessary and sufficient conditions for the convergence of the distributions of random sequences with independent random indices (including sums of a random number of random vectors and multivariate statistics constructed from samples with random sizes) to scale mixtures of multivariate elliptically contoured stable distributions. The property of scale-mixed multivariate elliptically contoured stable distributions to be both scale mixtures of a non-trivial multivariate stable distribution and a normal scale mixture is used to obtain necessary and sufficient conditions for the convergence of the distributions of random sums of random vectors with covariance matrices to the multivariate generalized Linnik distribution.

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43

Prokopchina, Svetlana V. "ON THE QUESTION OF DETERMINING THE PROBABILITY DENSITY OF TYPICAL DISTRIBUTIONS FROM EXPERIMENTAL DATA." SOFT MEASUREMENTS AND COMPUTING 7/2, no. 68 (2023): 5–13. http://dx.doi.org/10.36871/2618-9976.2023.07-2.001.

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The article discusses the issues of determining errors in determining the type of distributions. The type of distributions is expressed in the form of probability densities of unimodal distribution laws of the K. Pearson system. Analytical dependences are obtained to determine the necessary volumes of sample data to ensure the required accuracy of identification and approximation of these distribution laws. Specific analytical dependences and graphs are given for determining such distribution laws as simple laws (normal, uniform, triangular) probability distributions, oneparameter laws (gamma distributions, lognormal distribution, Weibull distribution), twoparameter beta distribution.

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Roshni, C., D. Venkatesan, and C. B. Prasanth. "A Generalized Area-Biased Power Ishita Distribution - Properties and Applications." Indian Journal Of Science And Technology 17, no. 29 (2024): 3037–43. http://dx.doi.org/10.17485/ijst/v17i29.1515.

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Objectives: Generalized Area-Biased Power Ishita Distribution (GAPID) is a brand-new distribution that was suggested in this study. Its characterization is also mentioned in detail. Methods: The idea of weighted distributions is incorporated. This helps to derive new distributions that will be a best fit for many real-life data from many domains like agriculture, biomedical, financial, etc., where they may not match with the conventional distributions. Thus, it becomes necessary to create new distributions. The parameters have been calculated by maximum likelihood estimation. Findings: Its hazard rate function, survival function, and Moments, among other statistical features, were explored. Novelty: As results from classical distributions are insufficient for many Biomedical datasets, this novel distribution was fitted to a real data set of lung cancer patients' survival periods in months, allowing for a discussion of the data set's use. The superiority of the distribution is tested by comparing the same with known distributions and finding this one is better. Thereby the importance of the said distribution is established. Keywords: Estimate, Weighted distributions, Parameters, Reliability, Ishita distribution

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45

Roychowdhury, Mrinal Kanti, and Wasiela Salinas. "Quantization for a Mixture of Uniform Distributions Associated with Probability Vectors." Uniform distribution theory 15, no. 1 (2020): 105–42. http://dx.doi.org/10.2478/udt-2020-0006.

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AbstractThe basic goal of quantization for probability distribution is to reduce the number of values, which is typically uncountable, describing a probability distribution to some finite set and thus approximation of a continuous probability distribution by a discrete distribution. Mixtures of probability distributions, also known as mixed distributions, are an exciting new area for optimal quantization. In this paper, we investigate the optimal quantization for three different mixed distributions generated by uniform distributions associated with probability vectors.

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46

Boakye, Abraham Bamfo, Suleman Nasiru, and Sampson Wiredu. "New family of distributions based on the unit modified Burr III distribution." Journal of Statistics and Management Systems 27, no. 6 (2024): 1199–220. http://dx.doi.org/10.47974/jsms-1239.

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In recent times, there has been significant attention to the improvements to classical probability distributions in the literature. Because of this attention, many probability generators or family distribution functions have emerged. These generators can control the skewness, kurtosis, and tail weight of datasets effectively. The unit modified Burr III family of distributions—an entirely new family of distributions—has been developed. The mathematical and statistical characteristics of this new family have been derived. Two special distributions, the unit modified Burr III Weibull (UMBIIIW) and unit modified Burr III Chen (UMBIIIC) distributions, have been developed from this family. These distributions’ parameters have been estimated using the maximum likelihood estimation (MLE) technique. A simulation method based on Monte-Carlo was employed to investigate the behavior of these estimators. Next, a real-life dataset was used to demonstrate the UMBIIIC distribution’s applicability. Finally, an entirely new regression equation, called the log unit modified Burr III Weibull (LUMBIIIW) regression equation, was proposed, and real-life data were used to demonstrate how applicable it is. With the data used in the application illustration, the new regression equation offers the best fit among its competitive models.

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C M, Latha, and Sandhya E. "CG and CEG Distributions with Uniform Secondary Distribution." International Journal of Scientific and Research Publications (IJSRP) 9, no. 12 (2019): p9635. http://dx.doi.org/10.29322/ijsrp.9.12.2019.p9635.

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48

Dahel, S., and N. Giri. "Some distributions related to a noncentral wishart distribution." Communications in Statistics - Theory and Methods 23, no. 1 (1994): 229–37. http://dx.doi.org/10.1080/03610929408831249.

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Pudovkin, Alexander I., and Lutz Bornmann. "Approximation of citation distributions to the Poisson distribution." COLLNET Journal of Scientometrics and Information Management 12, no. 1 (2018): 49–53. http://dx.doi.org/10.1080/09737766.2017.1332605.

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Nadarajah, Saralees, and Samuel Kotz. "Sampling distributions associated with the multivariate t distribution." Statistica Neerlandica 59, no. 2 (2005): 214–34. http://dx.doi.org/10.1111/j.1467-9574.2005.00288.x.

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