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On Arnold–Villasenor Conjectures For Characterizaing Exponential Distribution Based On Sample Of Size Three, George Yanev
On Arnold–Villasenor Conjectures For Characterizaing Exponential Distribution Based On Sample Of Size Three, George Yanev
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
Arnold and Villasenor [4] obtain a series of characterizations of the exponential distribution based on random samples of size two. These results were already applied in constructing goodness-of-fit tests. Extending the techniques from [4], we prove some of Arnold and Villasenor’s conjectures for samples of size three. An example with simulated data is discussed.
The Marshall-Olkin Exponentiated Generalized G Family Of Distributions: Properties, Applications, And Characterizations, Haitham M. Yousof, Mahdi Rasekhi, Morad Alizadeh, Gholamhossein Hamedani
The Marshall-Olkin Exponentiated Generalized G Family Of Distributions: Properties, Applications, And Characterizations, Haitham M. Yousof, Mahdi Rasekhi, Morad Alizadeh, Gholamhossein Hamedani
Mathematical and Statistical Science Faculty Research and Publications
In this paper, we propose and study a new class of continuous distributions called the Marshall-Olkin exponentiated generalized G (MOEG-G) family which extends the Marshall-Olkin-G family introduced by Marshall and Olkin [A. W. Marshall, I. Olkin, Biometrika 84 (1997), 641-652]. Some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, generating function, order statistics and probability weighted moments are derived. Some characteristics of the new family are presented. Maximum likelihood estimation for the model parameters under uncensored and censored data is addressed in Section 5 as well as a simulation study to assess the performance of …
Odd Generalized N-H Generated Family Of Distributions With Application To Exponential Model, Zubair Ahmad, M. Elgarhy, Gholamhossein Hamedani, Nadeem Shafique Butt
Odd Generalized N-H Generated Family Of Distributions With Application To Exponential Model, Zubair Ahmad, M. Elgarhy, Gholamhossein Hamedani, Nadeem Shafique Butt
Mathematical and Statistical Science Faculty Research and Publications
A new family of distributions called the odd generalized N-H is introduced and studied. Four new special models are presented. Some mathematical properties of the odd generalized N-H family are studied. Explicit expressions for the moments, probability weighted, quantile function, mean deviation, order statistics and Rényi entropy are investigated. Characterizations based on the truncated moments, hazard function and conditional expectations are presented for the generated family. Parameter estimates of the family are obtained based on maximum likelihood procedure. Two real data sets are employed to show the usefulness of the new family.
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.
The Price Is Right: Analyzing Bidding Behavior On Contestants’ Row, Paul Kvam
The Price Is Right: Analyzing Bidding Behavior On Contestants’ Row, Paul Kvam
Department of Math & Statistics Faculty Publications
The TV game show “The Price is Right” features a bidding auction called Contestant’s Row that rewards the player (out of four) who bids closest to an item’s value without overbidding. By exploring 903 game outcomes from the 2000–2001 season, we show how player strategies are significantly inefficient, and compare the empirical results to probability outcomes for optimal bid strategies found in a recent study. Findings show that the last bidder would do better using the naïve strategy of bidding a dollar more than the highest of the three bids. We apply the EM algorithm in a novel way to …
On The Exponentiated Weibull Rayleigh Distribution, Mohammed Elgarhy, Ibrahim Elbatal, Gholamhossein G. Hamedani, Amal Hassan
On The Exponentiated Weibull Rayleigh Distribution, Mohammed Elgarhy, Ibrahim Elbatal, Gholamhossein G. Hamedani, Amal Hassan
Mathematical and Statistical Science Faculty Research and Publications
A new four-parameter probability model, referred to the exponentiated Weibull Rayleigh (EWR) distribution, is introduced. Essential statistical properties of the distribution are considered. The maximum likelihood estimators of population parameters are given in case of complete sample. Simulation study is carried out to estimate the model parameters of EWR distribution. Additionally, parameter estimators are given in case of Type II censored samples. We come up with two applications to confirm the usefulness of the proposed distribution.
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 …
On Rank Driven Dynamical Systems, J. J. P. Veerman, F. J. Prieto
On Rank Driven Dynamical Systems, J. J. P. Veerman, F. J. Prieto
Mathematics and Statistics Faculty Publications and Presentations
We investigate a class of models related to the Bak-Sneppen model, initially proposed to study evolution. The BS model is extremely simple and yet captures some forms of “complex behavior” such as self-organized criticality that is often observed in physical and biological systems. In this model, random fitnesses in [0, 1] are associated to agents located at the vertices of a graph G. Their fitnesses are ranked from worst (0) to best (1). At every time-step the agent with the worst fitness and some others with a priori given rank probabilities are replaced by new agents with random fitnesses. We …
Expected Efficiency Ranks From Parametric Stochastic Frontier Models, William C. Horrace, Seth Richards-Shubik
Expected Efficiency Ranks From Parametric Stochastic Frontier Models, William C. Horrace, Seth Richards-Shubik
Center for Policy Research
In the stochastic frontier model we extend the multivariate probability statements of Horrace (2005) to calculate the conditional probability that a firm is any particular efficiency rank in the sample. From this we construct the conditional expected efficiency rank for each firm. Compared to the traditional ranked efficiency point estimates, firm-level conditional expected ranks are more informative about the degree of uncertainty of the ranking. The conditional expect ranks may be useful for empiricists. A Monte Carlo study and an empirical example are provided.
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.
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].
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.
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.
Asymptotic Reliability Rheory Of K-Out-Of-N Systems, Nuria Torrado, J. J. P. Veerman
Asymptotic Reliability Rheory Of K-Out-Of-N Systems, Nuria Torrado, J. J. P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
We formulate a theory that allows us to formulate a simple criterion that ensures that two k-out-of-n systems A and are not ordered. If the systems fail the criterion, it does not follow they are ordered. Thus the theory only serves to avoid some a priori useless comparisons: when neither A nor can be said to be better than the other. The power of the theory lies in its wide potential applicability: the assumptions involve very weak estimates on the asymptotic behavior (as t→0 and as t→∞) of the constituent survival probabilities. We include examples.
Comparing Hall Of Fame Baseball Players Using Most Valuable Player Ranks, Paul Kvam
Comparing Hall Of Fame Baseball Players Using Most Valuable Player Ranks, Paul Kvam
Department of Math & Statistics Faculty Publications
We propose a rank-based statistical procedure for comparing performances of top major league baseball players who performed in different eras. The model is based on using the player ranks from voting results for the most valuable player awards in the American and National Leagues. The current voting procedure has remained the same since 1932, so the analysis regards only data for players whose career blossomed after that time. Because the analysis is based on quantiles, its basis is nonparametric and relies on a simple link function. Results are stratified by fielding position, and we compare 73 Hall of Fame players …
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.
Smooth Quantile Ratio Estimation, Francesca Dominici, Leslie Cope, Daniel Q. Naiman, Scott L. Zeger
Smooth Quantile Ratio Estimation, Francesca Dominici, Leslie Cope, Daniel Q. Naiman, Scott L. Zeger
Johns Hopkins University, Dept. of Biostatistics Working Papers
In a study of health care expenditures attributable to smoking, we seek to compare the distribution of medical costs for persons with lung cancer or chronic obstructive pulmonary disease (cases) to those without (controls) using a national survey which includes hundreds of cases and thousands of controls. The distribution of costs is highly skewed toward larger values, making estimates of the mean from the smaller sample dependent on a small fraction of the biggest values. One approach to deal with the smaller sample is to rely on a simple parametric model such as the log-normal, but this makes the undesirable …
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 …