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- Department of Math & Statistics Faculty Publications (4)
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The Poisson Topp Leone Generator Of Distributions For Lifetime Data: Theory, Characterizations And Applications, Faton Merovci, Haitham M. Yousof, Gholamhossein Hamedani
The Poisson Topp Leone Generator Of Distributions For Lifetime Data: Theory, Characterizations And Applications, Faton Merovci, Haitham M. Yousof, Gholamhossein Hamedani
Mathematical and Statistical Science Faculty Research and Publications
We study a new family of distributions defined by the minimum of the Poisson random number of independent identically distributed random variables having a Topp Leone-G distribution (see Rezaei et al., (2016)). Some mathematical properties of the new family including ordinary and incomplete moments, quantile and generating functions, mean deviations, order statistics, reliability and entropies are derived. Maximum likelihood estimation of the model parameters is investigated. Some special models of the new family are discussed. An application is carried out on real data set applications sets to show the potentiality of the proposed family.
A Probability Model For Strategic Bidding On The Price Is Right, Paul H. Kvam
A Probability Model For Strategic Bidding On The Price Is Right, Paul H. Kvam
Department of Math & Statistics Faculty Publications
The TV game show “The Price is Right” features a bidding auction called “Contestants’ Row” that rewards the player (out of 4) who bids closest to an item’s value, without overbidding. This paper considers ways in which players can maximize a winning probability based on the player's bidding order. We consider marginal strategies in which players assume opponents are bidding individually perceived values of the merchandise. Based on preceding bids of others, players have information available to create strategies. We consider conditional strategies in which players adjust bids knowing other players are using strategies. The last bidder has a large …
On Characterizations And Infinite Divisibility Of Recently Introduced Distributions, Gholamhossein G. Hamedani
On Characterizations And Infinite Divisibility Of Recently Introduced Distributions, Gholamhossein G. Hamedani
Mathematics, Statistics and Computer Science Faculty Research and Publications
We present here characterizations of the most recently introduced continuous univariate distributions based on: (i) a simple relationship between two truncated moments; (ii) truncated moments of certain functions of the 1th order statistic; (iii) truncated moments of certain functions of the nth order statistic; (iv) truncated moment of certain function of the random variable. We like to mention that the characterization (i) which is expressed in terms of the ratio of truncated moments is stable in the sense of weak convergence. We will also point out that some …
On Six-Parameter Fréchet Distribution: Properties And Applications, Haitham M. Yousof, Ahmed Z. Afify, Abd El Hadi N. Ebraheim, Gholamhossein G. Hamedani, Nadeem Shafique Butt
On Six-Parameter Fréchet Distribution: Properties And Applications, Haitham M. Yousof, Ahmed Z. Afify, Abd El Hadi N. Ebraheim, Gholamhossein G. Hamedani, Nadeem Shafique Butt
Mathematics, Statistics and Computer Science Faculty Research and Publications
This paper introduces a new generalization of the transmuted Marshall-Olkin Fréchet distribution of Afify et al. (2015), using Kumaraswamy generalized family. The new model is referred to as Kumaraswamy transmuted Marshall-Olkin Fréchet distribution. This model contains sixty two sub-models as special cases such as the Kumaraswamy transmuted Fréchet, Kumaraswamy transmuted Marshall-Olkin, generalized inverse Weibull and Kumaraswamy Gumbel type II distributions, among others. Various mathematical properties of the proposed distribution including closed forms for ordinary and incomplete moments, quantile and generating functions and Rényi and η-entropies are derived. The unknown parameters of the new distribution are estimated using the maximum …
Some Remarks On Arslan’S 2011 Paper, Gholamhossein Hamedani, Hans Volkmer
Some Remarks On Arslan’S 2011 Paper, Gholamhossein Hamedani, Hans Volkmer
Mathematics, Statistics and Computer Science Faculty Research and Publications
It is shown that the main theorem of Arslan’s paper (Theorem 2, 2011), as stated, is incorrect. Under additional conditions, we present a short proof of the corrected version of the theorem. We also give a proof of a theorem of Rao and Shanbhag (1991), employed by Arslan, without the use of the Kolmogorov Consistency Theorem.
Characterizations Of Exponential Distribution Based On Sample Of Size Three, George Yanev, Santanu Chakraborty
Characterizations Of Exponential Distribution Based On Sample Of Size Three, George Yanev, Santanu Chakraborty
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
Two characterizations of the exponential distribution based on equalities among order statistics in a random sample of size three are proved. This proves two conjectures stated recently in Arnold and Villasenor [4].
On Characterizations Of Exponential Distribution Through Order Statistics And Record Values With Random Shifts, M. Ahsanullah, Imtiyaz A. Shah, George Yanev
On Characterizations Of Exponential Distribution Through Order Statistics And Record Values With Random Shifts, M. Ahsanullah, Imtiyaz A. Shah, George Yanev
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
Distributional relations of the form Y d= X +T where X, Y, and T are record values or order statistics and the random translator T is independent from X are considered. Characterizations of the exponential distribution when the ordered random variables are non-neighboring are proved. Corollaries for Pareto and power function distributions are also derived.
Stochastic Comparisons Of Order Statistics And Spacings: A Review, Subhash C. Kochar
Stochastic Comparisons Of Order Statistics And Spacings: A Review, Subhash C. Kochar
Mathematics and Statistics Faculty Publications and Presentations
We review some of the recent developments in the area of stochastic comparisons of order statistics and sample spacings. We consider the cases when the parent observations are identically as well as nonidentically distributed. But most of the time we will be assuming that the observations are independent. The case of independent exponentials with unequal scale parameters as well as the proportional hazard rate model is discussed in detail.
Some Recent Results On Stochastic Comparisons And Dependence Among Order Statistics In The Case Of Phr Model, Subhash C. Kochar, Maochao Xu
Some Recent Results On Stochastic Comparisons And Dependence Among Order Statistics In The Case Of Phr Model, Subhash C. Kochar, Maochao Xu
Mathematics and Statistics Faculty Publications and Presentations
This paper reviews some recent results on stochastic orders and dependence among order statistics when the observations are independent and follow the proportional hazard rates model.
Nonparametric Estimation Of A Distribution Subject To A Stochastic Precedence Constraint, Miguel A. Arcones, Paul H. Kvam, Francisco J. Samaniego
Nonparametric Estimation Of A Distribution Subject To A Stochastic Precedence Constraint, Miguel A. Arcones, Paul H. Kvam, Francisco J. Samaniego
Department of Math & Statistics Faculty Publications
For any two random variables X and Y with distributions F and G defined on [0,∞), X is said to stochastically precede Y if P(X≤Y) ≥ 1/2. For independent X and Y, stochastic precedence (denoted by X≤spY) is equivalent to E[G(X–)] ≤ 1/2. The applicability of stochastic precedence in various statistical contexts, including reliability modeling, tests for distributional equality versus various alternatives, and the relative performance of comparable tolerance bounds, is discussed. The problem of estimating the underlying distribution(s) of experimental data under the assumption that they obey a …
Ranked Set Sampling From Location-Scale Families Of Symmetric Distributions, Ram C. Tiwari, Paul H. Kvam
Ranked Set Sampling From Location-Scale Families Of Symmetric Distributions, Ram C. Tiwari, Paul H. Kvam
Department of Math & Statistics Faculty Publications
Statistical inference based on ranked set sampling has primarily been motivated by nonparametric problems. However, the sampling procedure can provide an improved estimator of the population mean when the population is partially known. In this article, we consider estimation of the population mean and variance for the location-scale families of distributions. We derive and compare different unbiased estimators of these parameters based on independent replications of a ranked set sample of size n. Large sample properties, along with asymptotic relative efficiencies, help identify which estimators are best suited for different location-scale distributions.
Fisher Information In Weighted Distributions, Satish Iyengar, Paul H. Kvam, Harshinder Singh
Fisher Information In Weighted Distributions, Satish Iyengar, Paul H. Kvam, Harshinder Singh
Department of Math & Statistics Faculty Publications
Standard inference procedures assume a random sample from a population with density fμ(x) for estimating the parameter μ. However, there are many applications in which the available data are a biased sample instead. Fisher modeled biased sampling using a weight function w(x) ¸ 0, and constructed a weighted distribution with a density fμw(x) that is proportional to w(x)fμ(x). In this paper, we assume that fμ(x) belongs to an exponential family, and study the Fisher information about μ in observations obtained from some commonly arising weighted distributions: (i) the kth order …