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Journal articles on the topic 'Asymptotic distribution'

Author: Grafiati

Published: 4 June 2021

Last updated: 11 June 2025

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1

Miyazawa, Masakiyo. "Martingale approach for tail asymptotic problems in the generalized Jackson network." Probability and Mathematical Statistics 37, no. 2 (2018): 395–430. http://dx.doi.org/10.19195/0208-4147.37.2.11.

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MARTINGALE APPROACH FOR TAIL ASYMPTOTIC PROBLEMS IN THE GENERALIZED JACKSON NETWORKWe study the tail asymptotic of the stationary joint queue length distribution for a generalized Jackson network GJN for short, assumingits stability. For the two-station case, this problem has recently been solved in the logarithmic sense for the marginal stationary distributions under the setting that arrival processes and service times are of phase-type. In this paper, we study similar tail asymptotic problems on the stationary distribution, but problems and assumptions are different. First, the asymptotics are studied not only for the marginal distribution but also the stationary probabilities of state sets of small volumes. Second, the interarrival and service times are generally distributed and light tailed, but of phase-type in some cases. Third, we also study the case that there are more than two stations, although the asymptotic results are less complete. For them, we develop a martingale method, which has been recently applied to a single queue with many servers by the author.

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2

WANG, Frank Xuyan. "Shape Factor Asymptotic Analysis I." Journal of Advanced Studies in Finance 11, no. 2 (2020): 108. http://dx.doi.org/10.14505//jasf.v11.2(22).05.

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We proposed using shape factor to distinguish probability distributions, and using relative minimum or maximum values of shape factor to locate distribution parameter allowable ranges for distribution fitting in our previous study. In this paper, the shape factor asymptotic analysis is employed to study such conditional minimum or maximum, to cross validate results found from numerical study and empirical formula we obtained and published earlier. The shape factor defined as kurtosis divided by skewness squared is characterized as the unique maximum choice of among all factors that is greater than or equal to 1 for all probability distributions. For all distributions from a specific distribution family, there may exists such that. The least upper bound of all such is defined as the distribution family’s characteristic number. The useful extreme values of the shape factor for various distributions that are found numerically before, the Beta, Kumaraswamy, Weibull, and GB2 distributions are derived using asymptotic analysis. The match of the numerical and the analytical results may arguably be considered proof of each other. The characteristic numbers of these distributions are also calculated. The study of the extreme value of the shape factor, or the shape factor asymptotic analysis, help reveal properties of the original shape factor, and reveal relationship between distributions, such as that between the Kumaraswamy distribution and the Weibull distribution.

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3

KUMAR, C. SATHEESH, and G. V. ANILA. "Asymptotic curved normal distribution." Journal of Statistical Research 52, no. 2 (2019): 173–86. http://dx.doi.org/10.47302/2018520204.

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Here we introduce a new class of skew normal distribution as a generalization of the extended skew curved normal distribution of Kumar and Anusree (J. Statist. Res., 2017) and investigate some of its important statistical properties. The location-scale extension of the proposed class of distribution is also defined and discussed the estimation of its parameters by method of maximum likelihood. Further, a real life data set is considered for illustrating the usefulness of the model and a brief simulation study is attempted for assessing the performance of the estimators.

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Shimizu, Eiji, and Hiroshi Shiraishi. "An asymptotic distribution of compound Poisson distribution." Cogent Mathematics 3, no. 1 (2016): 1221614. http://dx.doi.org/10.1080/23311835.2016.1221614.

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5

Tanaka, Katsuto. "Asymptotic expansions for time series statistics." Journal of Applied Probability 23, A (1986): 211–27. http://dx.doi.org/10.2307/3214354.

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Asymptotic expansions for the distributions of estimators and test statistics are derived in connection with time series models. The expansions relate to marginal and joint distributions together with the percentiles of marginal distributions. We also consider transforming a statistic so that the transformed statistic has a distribution that coincides with its asymptotic distribution up to a higher order.

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Tanaka, Katsuto. "Asymptotic expansions for time series statistics." Journal of Applied Probability 23, A (1986): 211–27. http://dx.doi.org/10.1017/s0021900200117097.

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Asymptotic expansions for the distributions of estimators and test statistics are derived in connection with time series models. The expansions relate to marginal and joint distributions together with the percentiles of marginal distributions. We also consider transforming a statistic so that the transformed statistic has a distribution that coincides with its asymptotic distribution up to a higher order.

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7

Kahounová, Jana. "Asymptotic Probability Distribution of Sample Maximum." Acta Oeconomica Pragensia 16, no. 3 (2008): 40–46. http://dx.doi.org/10.18267/j.aop.103.

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8

Lyons, Russell. "Mixing and asymptotic distribution modulo 1." Ergodic Theory and Dynamical Systems 8, no. 4 (1988): 597–619. http://dx.doi.org/10.1017/s0143385700004715.

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AbstractIf μ is a probability measure which is invariant and ergodic with respect to the transformationx↦qxon the circle ℝ/ℤ, then according to the ergodic theorem, {qnx} has the asymptotic distribution μ for μ-a.e.x. On the other hand, Weyl showed that when μ is Lebesgue measure, λ, and {mj} is an arbitrary sequence of integers increasing strictly to ∞, the asymptotic distribution of {mjx} is λ for λ-a.e.x. Here, we investigate the asymptotic distributions of {mjx} μ-a.e. for fairly arbitrary {mj} under some strong mixing conditions on μ. The result is a kind of stable ergodicity: the distributions are obtained from simple operations applied to μ. The ideas extend to the situation of a sequence of transformationsx↦qnxwhere invariance is not present. This gives us information about many Riesz products and Bernoulli convolutions. Finally, we apply the theory to resolve some questions aboutH-sets.

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9

Coffman, Donna L., Alberto Maydeu-Olivares, and Jaume Arnau. "Asymptotic Distribution Free Interval Estimation." Methodology 4, no. 1 (2008): 4–9. http://dx.doi.org/10.1027/1614-2241.4.1.4.

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Abstract. Confidence intervals for the intraclass correlation coefficient (ICC) have been proposed under the assumption of multivariate normality. We propose confidence intervals which do not require distributional assumptions. We performed a simulation study to assess the coverage rates of normal theory (NT) and asymptotically distribution free (ADF) intervals. We found that the ADF intervals performed better than the NT intervals when kurtosis was greater than 4. When violations of distributional assumptions were not too severe, both the intervals performed about the same. The point estimate of the ICC was robust to distributional violations. We provide R code for computing the ADF confidence intervals for the ICC.

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10

Barral, Julien, and Yan-Hui Qu. "Multifractals in Weyl asymptotic distribution." Nonlinearity 24, no. 10 (2011): 2785–811. http://dx.doi.org/10.1088/0951-7715/24/10/008.

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11

Li, Jiexiang. "Asymptotic distribution of local medians." Journal of Nonparametric Statistics 20, no. 2 (2008): 175–85. http://dx.doi.org/10.1080/10485250801948286.

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12

Götze, F., and A. N. Tikhomirov. "Asymptotic Distribution of Quadratic Forms." Annals of Probability 27, no. 2 (1999): 1072–98. http://dx.doi.org/10.1214/aop/1022677395.

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13

Antonelli, Sabrina, and Giuliana Regoli. "Asymptotic distribution of density ratios." Statistics & Probability Letters 79, no. 3 (2009): 289–94. http://dx.doi.org/10.1016/j.spl.2008.08.009.

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14

Fukaya, Tomohiro, and Masaki Tsukamoto. "Asymptotic distribution of critical values." Geometriae Dedicata 143, no. 1 (2009): 63–67. http://dx.doi.org/10.1007/s10711-009-9372-3.

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15

Pollicott, Mark. "Asymptotic distribution of closed geodesics." Israel Journal of Mathematics 52, no. 3 (1985): 209–24. http://dx.doi.org/10.1007/bf02786516.

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16

Garunkštis, Ramūnas, and Laima Kaziulytė. "Asymptotic distribution of Beurling integers." International Journal of Number Theory 14, no. 10 (2018): 2555–69. http://dx.doi.org/10.1142/s179304211850152x.

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We study generalized prime systems [Formula: see text] and generalized integer systems [Formula: see text] obtained from them. The asymptotic distribution of generalized integers is deduced assuming that the generalized prime counting function [Formula: see text] behaves as [Formula: see text] for some [Formula: see text] and [Formula: see text].

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17

Abate, Joseph, and Ward Whitt. "Limits and Approximations for the Busy-Period Distribution in Single-Server Queues." Probability in the Engineering and Informational Sciences 9, no. 4 (1995): 581–602. http://dx.doi.org/10.1017/s0269964800004071.

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Limit theorems are established and relatively simple closed-form approximations are developed for the busy-period distribution in single-server queues. For the M/G/l queue, the complementary busy-period c.d.f. is shown to be asymptotically equivalent as t → ∞ to a scaled version of the heavy-traffic limit (obtained as p → 1), where the scaling parameters are based on the asymptotics as t → ∞. We call this the asymptotic normal approximation, because it involves the standard normal c.d.f. and density. The asymptotic normal approximation is asymptotically correct as t → ∞ for each fixed p and as p → 1 for each fixed t and yields remarkably good approximations for times not too small, whereas the direct heavy-traffic (p → 1) and asymptotic (t → ∞) limits do not yield such good approximations. Indeed, even the approximation based on three terms of the standard asymptotic expansion does not perform well unless t is very large. As a basis for generating corresponding approximations for the busy-period distribution in more general models, we also establish a more general heavy-traffic limit theorem.

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18

Gleaton, James, Ping Sa, and Sami Hamid. "Asymptotic Properties of MLE's for Distributions Generated from an Exponential Distribution by a Generalized Log-Logistic Transformation." Journal of Probability and Statistical Science 20, no. 1 (2022): 204–27. http://dx.doi.org/10.37119/jpss2022.v20i1.543.

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ABSTRACT. A generalized log-logistic (GLL) family of lifetime distributions is one in which any pair of distributions are related through a GLL transformation, for some (non-negative) value of the transformation parameter k (the odds function of the second distribution is the k-th power of the odds function of the first distribution). We consider GLL families generated from an exponential distribution. It is shown that the Maximum Likelihood Estimators (MLE’s) for the parameters of the generated, or composite, distribution have the properties of strong consistency and asymptotic normality and efficiency. Data simulation is also found to support the condition of asymptotic efficiency.   Keywords Generalized log-logistic exponential distribution; asymptotic properties of MLE’s; simulation

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19

Chen, Chao-Ping, та H. M. Srivastava. "Complete asymptotic expansions related to the probability density function of the χ2-distribution". Applicable Analysis and Discrete Mathematics, № 00 (2022): 15. http://dx.doi.org/10.2298/aadm210720015c.

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In this paper, we consider the function fp(t) = ? 2p?2(?2pt + p;p), where ?2(x;n) defined by ?2(x;p) = 2?p/2/?(p/2) e?x/2xp/2?1, is the density function of a ?2-distribution with n degrees of freedom. The asymptotic expansion of fp(t) for p ? ?, where p is not necessarily an integer, is obtained by an application of the standard asymptotics of ln ?(x). Two different methods of obtaining the coefficients in the asymptotic expansion are presented, which involve the use of the Bell polynomials.

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20

Moers, Michael. "Hypothesis Testing in a Fractional Ornstein-Uhlenbeck Model." International Journal of Stochastic Analysis 2012 (November 10, 2012): 1–23. http://dx.doi.org/10.1155/2012/268568.

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Consider an Ornstein-Uhlenbeck process driven by a fractional Brownian motion. It is an interesting problem to find criteria for whether the process is stable or has a unit root, given a finite sample of observations. Recently, various asymptotic distributions for estimators of the drift parameter have been developed. We illustrate through computer simulations and through a Stein's bound that these asymptotic distributions are inadequate approximations of the finite-sample distribution for moderate values of the drift and the sample size. We propose a new model to obtain asymptotic distributions near zero and compute the limiting distribution. We show applications to regression analysis and obtain hypothesis tests and their asymptotic power.

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21

De Michele. "Advances in Deriving the Exact Distribution of Maximum Annual Daily Precipitation." Water 11, no. 11 (2019): 2322. http://dx.doi.org/10.3390/w11112322.

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Maximum annual daily precipitation does not attain asymptotic conditions. Consequently, the results of classical extreme value theory do not apply to this variable. This issue has raised concerns about the frequent use of asymptotic distributions to model the maximum annual daily precipitation and, at the same time, has rekindled interest in deriving and testing its exact (or non-asymptotic) distribution. In this review, we summarize and discuss results to date about the derivation of the exact distribution of maximum annual daily precipitation, with attention on compound/superstatistical distributions.

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22

Sengupta, Nandana, and Fallaw Sowell. "On the Asymptotic Distribution of Ridge Regression Estimators Using Training and Test Samples." Econometrics 8, no. 4 (2020): 39. http://dx.doi.org/10.3390/econometrics8040039.

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The asymptotic distribution of the linear instrumental variables (IV) estimator with empirically selected ridge regression penalty is characterized. The regularization tuning parameter is selected by splitting the observed data into training and test samples and becomes an estimated parameter that jointly converges with the parameters of interest. The asymptotic distribution is a nonstandard mixture distribution. Monte Carlo simulations show the asymptotic distribution captures the characteristics of the sampling distributions and when this ridge estimator performs better than two-stage least squares. An empirical application on returns to education data is presented.

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23

CHAUMOÎTRE, VINCENT, and MICHAL KUPSA. "ASYMPTOTICS FOR RETURN TIMES OF RANK-ONE SYSTEMS." Stochastics and Dynamics 05, no. 01 (2005): 65–73. http://dx.doi.org/10.1142/s0219493705001298.

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We give a condition for nonperiodic rank-one systems to have non-exponential asymptotic distribution (equal to 1[1,∞[) of return times along subsequences of cylinders. Applying this result to the staircase transformation, we derive mixing dynamical systems with non-exponential asymptotics. Moreover, we show for two columns rank-one systems unique asymptotic along full sequences of cylinders.

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24

Mitra, Abhimanyu, and Sidney I. Resnick. "Aggregation of rapidly varying risks and asymptotic independence." Advances in Applied Probability 41, no. 3 (2009): 797–828. http://dx.doi.org/10.1239/aap/1253281064.

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We study the tail behavior of the distribution of the sum of asymptotically independent risks whose marginal distributions belong to the maximal domain of attraction of the Gumbel distribution. We impose conditions on the distribution of the risks (X,Y) such that P(X+Y>x) ∼ (constant) P(X>x). With the further assumption of nonnegativity of the risks, the result is extended to more than two risks. We note a sufficient condition for a distribution to belong to both the maximal domain of attraction of the Gumbel distribution and the subexponential class. We provide examples of distributions which satisfy our assumptions. The examples include cases where the marginal distributions ofXandYare subexponential and also cases where they are not. In addition, the asymptotic behavior of linear combinations of such risks with positive coefficients is explored, leading to an approximate solution of an optimization problem which is applied to portfolio design.

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25

Mitra, Abhimanyu, and Sidney I. Resnick. "Aggregation of rapidly varying risks and asymptotic independence." Advances in Applied Probability 41, no. 03 (2009): 797–828. http://dx.doi.org/10.1017/s0001867800003566.

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We study the tail behavior of the distribution of the sum of asymptotically independent risks whose marginal distributions belong to the maximal domain of attraction of the Gumbel distribution. We impose conditions on the distribution of the risks (X, Y) such that P(X + Y &gt; x) ∼ (constant) P(X &gt; x). With the further assumption of nonnegativity of the risks, the result is extended to more than two risks. We note a sufficient condition for a distribution to belong to both the maximal domain of attraction of the Gumbel distribution and the subexponential class. We provide examples of distributions which satisfy our assumptions. The examples include cases where the marginal distributions of X and Y are subexponential and also cases where they are not. In addition, the asymptotic behavior of linear combinations of such risks with positive coefficients is explored, leading to an approximate solution of an optimization problem which is applied to portfolio design.

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26

Yin, Chuancun, and Junsheng Zhao. "Nonexponential asymptotics for the solutions of renewal equations, with applications." Journal of Applied Probability 43, no. 3 (2006): 815–24. http://dx.doi.org/10.1239/jap/1158784948.

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Nonexponential asymptotics for solutions of two specific defective renewal equations are obtained. These include the special cases of asymptotics for a compound geometric distribution and the convolution of a compound geometric distribution with a distribution function. As applications of these results, we study the asymptotic behavior of the demographic birth rate of females, the perpetual put option in mathematics of finance, and the renewal function for terminating renewal processes.

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27

Yin, Chuancun, and Junsheng Zhao. "Nonexponential asymptotics for the solutions of renewal equations, with applications." Journal of Applied Probability 43, no. 03 (2006): 815–24. http://dx.doi.org/10.1017/s0021900200002126.

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Nonexponential asymptotics for solutions of two specific defective renewal equations are obtained. These include the special cases of asymptotics for a compound geometric distribution and the convolution of a compound geometric distribution with a distribution function. As applications of these results, we study the asymptotic behavior of the demographic birth rate of females, the perpetual put option in mathematics of finance, and the renewal function for terminating renewal processes.

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28

Lee, Sunbok. "Detecting Differential Item Functioning Using the Logistic Regression Procedure in Small Samples." Applied Psychological Measurement 41, no. 1 (2016): 30–43. http://dx.doi.org/10.1177/0146621616668015.

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The logistic regression (LR) procedure for testing differential item functioning (DIF) typically depends on the asymptotic sampling distributions. The likelihood ratio test (LRT) usually relies on the asymptotic chi-square distribution. Also, the Wald test is typically based on the asymptotic normality of the maximum likelihood (ML) estimation, and the Wald statistic is tested using the asymptotic chi-square distribution. However, in small samples, the asymptotic assumptions may not work well. The penalized maximum likelihood (PML) estimation removes the first-order finite sample bias from the ML estimation, and the bootstrap method constructs the empirical sampling distribution. This study compares the performances of the LR procedures based on the LRT, Wald test, penalized likelihood ratio test (PLRT), and bootstrap likelihood ratio test (BLRT) in terms of the statistical power and type I error for testing uniform and non-uniform DIF. The result of the simulation study shows that the LRT with the asymptotic chi-square distribution works well even in small samples.

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29

Giamouridis, Daniel G., and Michael N. Tamvakis. "Asymptotic Distribution Expansions in Option Pricing." Journal of Derivatives 9, no. 4 (2002): 33–44. http://dx.doi.org/10.3905/jod.2002.319184.

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30

OZONUR, Deniz, Hatice Tül Kübra AKDUR, and Hülya BAYRAK. "Optimal Asymptotic Tests for Nakagami Distribution." Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22, Special (2018): 487. http://dx.doi.org/10.19113/sdufbed.32458.

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31

Patterson, S. "The asymptotic distribution of Kloosterman sums." Acta Arithmetica 79, no. 3 (1997): 205–19. http://dx.doi.org/10.4064/aa-79-3-205-219.

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32

Zaikin, A. A. "On asymptotic expansion of posterior distribution." Lobachevskii Journal of Mathematics 37, no. 4 (2016): 515–25. http://dx.doi.org/10.1134/s1995080216040181.

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33

Salicru, M., M. L. Menendez, D. Morales та L. Pardo. "Asymptotic distribution of (h, φ)-entropies". Communications in Statistics - Theory and Methods 22, № 7 (1993): 2015–31. http://dx.doi.org/10.1080/03610929308831131.

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34

Csorgo, Sandor, and David M. Mason. "The Asymptotic Distribution of Intermediate Sums." Annals of Probability 22, no. 1 (1994): 145–59. http://dx.doi.org/10.1214/aop/1176988852.

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35

Jiménez, Raúl, and Yongzhao Shao. "Asymptotic Distribution for Symmetric Spacing Statistics." Communications in Statistics - Theory and Methods 36, no. 1 (2007): 37–46. http://dx.doi.org/10.1080/03610920600966704.

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36

Finner, Helmut, Thorsten Dickhaus, and Markus Roters. "Asymptotic Tail Properties of Student'st-Distribution." Communications in Statistics - Theory and Methods 37, no. 2 (2008): 175–79. http://dx.doi.org/10.1080/03610920701649019.

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37

Falk, Michael, and Diana Tichy. "Asymptotic Conditional Distribution of Exceedance Counts." Advances in Applied Probability 44, no. 1 (2012): 270–91. http://dx.doi.org/10.1239/aap/1331216653.

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We investigate the asymptotic distribution of the number of exceedances amongdidentically distributed but not necessarily independent random variables (RVs) above a sequence of increasing thresholds, conditional on the assumption that there is at least one exceedance. Our results enable the computation of thefragility index, which represents the expected number of exceedances, given that there is at least one exceedance. Computed from the firstdRVs of a strictly stationary sequence, we show that, under appropriate conditions, the reciprocal of the fragility index converges to the extremal index corresponding to the stationary sequence asdincreases.

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38

Arcones, Miguel A. "Asymptotic distribution of regression M-estimators." Journal of Statistical Planning and Inference 97, no. 2 (2001): 235–61. http://dx.doi.org/10.1016/s0378-3758(00)00224-x.

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39

Csorgo, Sandor, Erich Haeusler, and David M. Mason. "The Asymptotic Distribution of Extreme Sums." Annals of Probability 19, no. 2 (1991): 783–811. http://dx.doi.org/10.1214/aop/1176990451.

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40

Csorgo, Sandor, Erich Haeusler, and David M. Mason. "The Asymptotic Distribution of Trimmed Sums." Annals of Probability 16, no. 2 (1988): 672–99. http://dx.doi.org/10.1214/aop/1176991780.

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41

Falk, Michael, and Diana Tichy. "Asymptotic Conditional Distribution of Exceedance Counts." Advances in Applied Probability 44, no. 01 (2012): 270–91. http://dx.doi.org/10.1017/s000186780000553x.

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We investigate the asymptotic distribution of the number of exceedances among d identically distributed but not necessarily independent random variables (RVs) above a sequence of increasing thresholds, conditional on the assumption that there is at least one exceedance. Our results enable the computation of the fragility index, which represents the expected number of exceedances, given that there is at least one exceedance. Computed from the first d RVs of a strictly stationary sequence, we show that, under appropriate conditions, the reciprocal of the fragility index converges to the extremal index corresponding to the stationary sequence as d increases.

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42

Gurevich, V. A. "Asymptotic distribution of minimum contrast estimators." Journal of Soviet Mathematics 39, no. 2 (1987): 2571–78. http://dx.doi.org/10.1007/bf01084965.

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43

Marklof, Jens. "The asymptotic distribution of Frobenius numbers." Inventiones mathematicae 181, no. 1 (2010): 179–207. http://dx.doi.org/10.1007/s00222-010-0245-z.

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44

Lubinsky, D. S., A. Sidi, and H. Stahl. "Asymptotic zero distribution of biorthogonal polynomials." Journal of Approximation Theory 190 (February 2015): 26–49. http://dx.doi.org/10.1016/j.jat.2014.01.001.

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45

Li, Yang, and Yongcheng Qi. "Asymptotic distribution of modularity in networks." Metrika 83, no. 4 (2019): 467–84. http://dx.doi.org/10.1007/s00184-019-00740-7.

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46

Kent, John T. "Asymptotic Expansions for the Bingham Distribution." Applied Statistics 36, no. 2 (1987): 139. http://dx.doi.org/10.2307/2347545.

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47

Sinharay, Sandip. "The Asymptotic Distribution of Ability Estimates." Journal of Educational and Behavioral Statistics 40, no. 5 (2015): 511–28. http://dx.doi.org/10.3102/1076998615606115.

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48

Bilodeau, Martin. "ASYMPTOTIC DISTRIBUTION OF THE LARGEST EIGENVALUE." Communications in Statistics - Simulation and Computation 31, no. 3 (2002): 357–73. http://dx.doi.org/10.1081/sac-120003847.

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49

Cressie, N., and S. N. Lahiri. "The Asymptotic Distribution of REML Estimators." Journal of Multivariate Analysis 45, no. 2 (1993): 217–33. http://dx.doi.org/10.1006/jmva.1993.1034.

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50

Nabli, H. "Performability: asymptotic distribution and moment computation." Computers & Mathematics with Applications 48, no. 1-2 (2004): 1–8. http://dx.doi.org/10.1016/j.camwa.2004.04.030.

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