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Journal articles on the topic 'Asymptotic distribution'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 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 a

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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

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3

Cook, Nicholas John. "Reliability of Extreme Wind Speeds Predicted by Extreme-Value Analysis." Meteorology 2, no. 3 (2023): 344–67. http://dx.doi.org/10.3390/meteorology2030021.

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The reliability of extreme wind speed predictions at large mean recurrence intervals (MRI) is assessed by bootstrapping samples from representative known distributions. The classical asymptotic generalized extreme value distribution (GEV) and the generalized Pareto (GPD) distribution are compared with a contemporary sub-asymptotic Gumbel distribution that accounts for incomplete convergence to the correct asymptote. The sub-asymptotic model is implemented through a modified Gringorten method for epoch maxima and through the XIMIS method for peak-over-threshold values. The mean bias error is sh

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4

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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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

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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8

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

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9

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 distrib

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10

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 distributio

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11

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

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12

Aly, Amany E. "Asymptotic Predictive Inference of Negative Lower Tail Index Distributions." Mathematica Slovaca 73, no. 5 (2023): 1301–16. http://dx.doi.org/10.1515/ms-2023-0095.

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ABSTRACT In this paper, the results of El-Adll et al. [Asymptotic prediction for future observations of a random sample of unknown continuous distribution, Complexity 2022 (2022), Art. ID 4073799], are extended to the lower negative tail index distributions. Three distinct estimators of the lower negative tail index are proposed, as well as an asymptotic confidence interval. Moreover, different asymptotic predictive intervals for future observations are constructed for distributions attracted to the lower extreme value distribution with a negative tail index. Furthermore, the asymptotic maximu

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13

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

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14

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

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15

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

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16

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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17

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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18

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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19

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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20

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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21

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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22

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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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

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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25

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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26

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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27

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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28

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 dist

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29

Melas, Vyacheslav B., and Dmitrii I. Salnikov. "On the asymptotic power of the “energy” test for equality of two distributions." Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy 11, no. 3 (2024): 477–88. http://dx.doi.org/10.21638/spbu01.2024.304.

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In the paper the asymptotic distribution and the formula for the asymptotic power are found for the "energy" test in the case of alternative distributions differ from zero distribution by the parameter of shift and/or the parameter of scale. This criterion is an alternative for the well-known Mann-Whitney test but allows to compare distributions that differ by the scale parameter. The efficiency of the results obtained is demonstrated by the stochastic simulation for the normal distribution and the Cauchy distribution.

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30

Abdullahi, Ibrahim, Usman Mukhtar, and Isyaku Muhammad. "On some Asymptotic Properties of the Extended Cosine Burr XII Distribution." UMYU Scientifica 3, no. 4 (2024): 369–76. https://doi.org/10.56919/usci.2434.031.

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Study’s Excerpt The extended cosine Burr XII (ECSBXII) distribution model developed within the extended cosine-G family is introduced. The asymptotic properties of the mean residual life (MRL) and extreme order statistics specific to the ECSBXII distribution are derived. Practical application of the asymptotic MRL is shown using simulation studies. Full Abstract In statistics, asymptotic functions provide a powerful framework for understanding the behavior of functions or statistical procedures within the limits of certain parameters. Also, in reliability, mean residual life assumes a critical

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31

Melas, Vyacheslav B. "On the asymptotic power of a method for testing hypothesis about equality of distributions." Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy 10, no. 2 (2023): 249–58. http://dx.doi.org/10.21638/spbu01.2023.206.

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The paper is devoted to studying the asymptotic power of a method for testing hypothesis on equality of two distributions that can be considered as a generalization of Mann - Whitney -Wilcoxon test. We consider a class of distributions such that the expection of the square of an auxiliary function is finite. For the case when alternative distribution differ from the initial one only by a shift the asymptotic distribution and asymptotic power of the test are found explicitly. Up to now the power of the test was studied only by stochastic simulation.

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32

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

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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 o

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Vasudeva, R., J. Vasantha Kumari, and S. Ravi. "On the Asymptotic Behaviour of Extremes and Near Maxima of Random Observations from the General Error Distributions." Journal of Applied Probability 51, no. 2 (2014): 528–41. http://dx.doi.org/10.1239/jap/1402578641.

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As the name suggests, the family of general error distributions has been used to model nonnormal errors in a variety of situations. In this article we show that the asymptotic distribution of linearly normalized partial maxima of random observations from the general error distributions is Gumbel when the parameter of these distributions lies in the interval (0, 1). Our result fills a gap in the literature. We also establish the corresponding density convergence, obtain an asymptotic distribution of the partial maxima under power normalization, and state and prove a strong law. We also study th

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Vasudeva, R., J. Vasantha Kumari, and S. Ravi. "On the Asymptotic Behaviour of Extremes and Near Maxima of Random Observations from the General Error Distributions." Journal of Applied Probability 51, no. 02 (2014): 528–41. http://dx.doi.org/10.1017/s0021900200011402.

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As the name suggests, the family of general error distributions has been used to model nonnormal errors in a variety of situations. In this article we show that the asymptotic distribution of linearly normalized partial maxima of random observations from the general error distributions is Gumbel when the parameter of these distributions lies in the interval (0, 1). Our result fills a gap in the literature. We also establish the corresponding density convergence, obtain an asymptotic distribution of the partial maxima under power normalization, and state and prove a strong law. We also study th

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36

Vamvakari, Malvina. "Asymptotic Behaviour of Univariate and Multivariate Absorption Distributions." RAIRO - Theoretical Informatics and Applications 58 (2024): 15. http://dx.doi.org/10.1051/ita/2024006.

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In this work we study the asymptotic behaviour of univariate, bivariate and multivariate absorption discrete q-distributions. Specifically, the pointwise convergence of the univariate absorption distribution to a deformed Gaussian distribution is established. Also, the pointwise convergence of the bivariate and multivariate absorption distributions to bivariate and multivariate deformed Gaussian ones respectively, are established Moreover, interesting applications of the asymptotic behaviour of univariate and multivariate absorption processes are presented.

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37

Zaidi, Ali A., B. Van Brunt, and G. C. Wake. "Solutions to an advanced functional partial differential equation of the pantograph type." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471, no. 2179 (2015): 20140947. http://dx.doi.org/10.1098/rspa.2014.0947.

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A model for cells structured by size undergoing growth and division leads to an initial boundary value problem that involves a first-order linear partial differential equation with a functional term. Here, size can be interpreted as DNA content or mass. It has been observed experimentally and shown analytically that solutions for arbitrary initial cell distributions are asymptotic as time goes to infinity to a certain solution called the steady size distribution. The full solution to the problem for arbitrary initial distributions, however, is elusive owing to the presence of the functional te

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38

Miyoshi, Naoto, and Tomoyuki Shirai. "Tail asymptotics of signal-to-interference ratio distribution in spatial cellular network models." Probability and Mathematical Statistics 37, no. 2 (2018): 431–53. http://dx.doi.org/10.19195/0208-4147.37.2.12.

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TAIL ASYMPTOTICS OF SIGNAL-TO-INTERFERENCE RATI ODISTRIBUTION IN SPATIAL CELLULAR NETWORK MODELSWe consider a spatial stochastic model of wireless cellular networks, where the base stations BSs are deployed according to a simple and stationary point process on Rd, d > 2. In this model, we investigate tail asymptotics of the distribution of signal-to-interference ratio SIR, which is a key quantity in wireless communications. In the case where the pathloss function representing signal attenuation is unbounded at the origin, we derive the exact tail asymptotics of the SIR distribution under an

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39

Angus, John E. "Some Asymptotic Analysis of Resistant Rules For Outlier Labeling." Probability in the Engineering and Informational Sciences 3, no. 1 (1989): 157–64. http://dx.doi.org/10.1017/s0269964800001042.

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Previous studies have examined the behavior of outlier detection rules for symmetric distributions that label as “outside” any observations that fall outside the interval [FL – k(Fu – FL), Fu + k(Fu – FL)], where FL and FU are functions of the order statistics estimating the 0.25 and 0.75 quantiles of the distribution underlying the i.i.d. sample. A measure of the performance of this type of rule is the “some-outside rate” per sample computed with respect to a given (usually Gaussian) null distribution. The “some-outside rate” (SOR) per sample is the probability that the sample will contain on

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40

Mata, Ana J. "Asymptotic Dependence of Reinsurance Aggregate Claim Amounts." ASTIN Bulletin 33, no. 02 (2003): 239–63. http://dx.doi.org/10.2143/ast.33.2.503692.

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In this paper we study the asymptotic behaviour of the joint distribution of reinsurance aggregate claim amounts for large values of the retention level under various dependence assumptions. We prove that, under certain dependence assumptions, for large values of the retention level the ratio between the joint distribution of the aggregate losses and the product of the marginal distributions converges to a constant value that only depends on the frequency parameters.

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Mata, Ana J. "Asymptotic Dependence of Reinsurance Aggregate Claim Amounts." ASTIN Bulletin 33, no. 2 (2003): 239–63. http://dx.doi.org/10.1017/s0515036100013453.

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In this paper we study the asymptotic behaviour of the joint distribution of reinsurance aggregate claim amounts for large values of the retention level under various dependence assumptions. We prove that, under certain dependence assumptions, for large values of the retention level the ratio between the joint distribution of the aggregate losses and the product of the marginal distributions converges to a constant value that only depends on the frequency parameters.

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42

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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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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44

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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45

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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46

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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47

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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48

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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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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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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Abstract:

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 inde

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