Showing papers in "Journal of Statistical Distributions and Applications in 2015"
TL;DR: A new family of continuous distributions called the odd generalized exponential family, whose hazard rate could be increasing, decreasing, J, reversed-J, bathtub and upside-down bathtub is proposed, which includes as a special case the widely known exponentiated-Weibull distribution.
Abstract: We propose a new family of continuous distributions called the odd generalized exponential family, whose hazard rate could be increasing, decreasing, J, reversed-J, bathtub and upside-down bathtub. It includes as a special case the widely known exponentiated-Weibull distribution. We present and discuss three special models in the family. Its density function can be expressed as a mixture of exponentiated densities based on the same baseline distribution. We derive explicit expressions for the ordinary and incomplete moments, quantile and generating functions, Bonferroni and Lorenz curves, Shannon and Renyi entropies and order statistics. For the first time, we obtain the generating function of the Frechet distribution. Two useful characterizations of the family are also proposed. The parameters of the new family are estimated by the method of maximum likelihood. Its usefulness is illustrated by means of two real lifetime data sets.
AMS Subject Classification Primary 60E05; secondary 62N05; 62F10
125 citations
TL;DR: A comprehensive survey of the different methods of generating discrete probability distributions as analogues of continuous probability distributions is presented along with their applications in construction of new discrete distributions.
Abstract: In this paper a comprehensive survey of the different methods of generating discrete probability distributions as analogues of continuous probability distributions is presented along with their applications in construction of new discrete distributions. The methods are classified based on different criterion of discretization.
105 citations
TL;DR: General mathematical properties of a new generator of continuous distributions with three extra shape parameters called the beta Marshall-Olkin family are studied and explicit expressions for the ordinary and incomplete moments, quantile and generating functions, Bonferroni and Lorenz curves, Shannon and Rényi entropies and order statistics are determined.
Abstract: We study general mathematical properties of a new generator of continuous distributions with three extra shape parameters called the beta Marshall-Olkin family. We present some special models and investigate the asymptotes and shapes. The new density function can be expressed as a mixture of exponentiated densities based on the same baseline distribution. We derive a power series for its quantile function. Explicit expressions for the ordinary and incomplete moments, quantile and generating functions, Bonferroni and Lorenz curves, Shannon and Renyi entropies and order statistics, which hold for any baseline model, are determined. We discuss the estimation of the model parameters by maximum likelihood and illustrate the flexibility of the family by means of two applications to real data. PACS 02.50.Ng, 02.50.Cw, 02.50.-r Mathematics Subject Classification (2010) 62E10, 60E05, 62P99
64 citations
TL;DR: In this article, a generalized Weibull family of distributions with two extra positive parameters was proposed to extend the normal, gamma, Gumbel and inverse Gausssian distributions, among several other well-known distributions.
Abstract: We propose a generalized Weibull family of distributions with two extra positive parameters to extend the normal, gamma, Gumbel and inverse Gausssian distributions, among several other well-known distributions. We provide a comprehensive treatment of its general mathematical properties including quantile and generating functions, ordinary and incomplete moments and other properties. We introduce the log-generalized Weibull-log-logistic, this is new regression model represents a parametric family of models that includes as sub-models several widely known regression models that can be applied to censored survival data. We discuss estimation of the model parameters by maximum likelihood and provide two applications to real data.
59 citations
TL;DR: This article provided a new perspective on why the Morgan-Pitman test does not control the probability of a Type I error when the marginal distributions have heavy tails and suggested an alternative method for testing the hypothesis of equal variances.
Abstract: Various methods have been derived that are designed to test the hypothesis that two dependent variables have a common variance. Extant results indicate that all of these methods perform poorly in simulations. The paper provides a new perspective on why the Morgan-Pitman test does not control the probability of a Type I error when the marginal distributions have heavy tails. This new perspective suggests an alternative method for testing the hypothesis of equal variances and simulations indicate that it continues to perform well in situations where the Morgan-Pitman test performs poorly.
27 citations
TL;DR: In this article, a moment-ratio diagram of the two-parameter Birnbaum-Saunders distribution is presented and several properties of the generalized model are compared to experimental data.
Abstract: The Birnbaum-Saunders distribution was derived in 1969 as a lifetime model for a specimen subjected to cyclic patterns of stresses and strains, and the ultimate failure of the specimen is assumed to be due to the growth of a dominant crack in the material. The inverse Gaussian distribution is used to describe the first passage time for a particle (moving with constant velocity) that is subject to linear Brownian motion. These two models have a rich history, and they have been shown to be much related. In this article, these two models will be reviewed and comparisons will be made. Specifically, two moment-ratio diagrams will be presented that gives insight to the reason of both distributions often achieve similar fits to experimental data. Next, a generalized Birnbaum-Saunders distribution, will be presented and several properties will be derived. In particular, it will be shown that this generalized model can be expressed as a mixture of inverse Gaussian-type random variables (similar to the two-parameter Birnbaum-Saunders model). Estimation of the parameters in the generalized Birnbaum-Saunders distribution will be discussed. Lastly, some conclusions from this investigation are presented.
14 citations
TL;DR: In this article, the problem of robust estimation for the two-parameter Birnbaum-Saunders distribution was studied and several estimators which have simple closed forms and are also robust to data contamination were proposed.
Abstract: We study the problem of robust estimation for the two-parameter Birnbaum-Saunders distribution. It is well known that the maximum likelihood estimator (MLE) is efficient when the underlying model is true but at the same time it is quite sensitive to data contamination that is often encountered in practice. In this paper, we propose several estimators which have simple closed forms and are also robust to data contamination. We study the breakdown points and asymptotic properties of the proposed estimators. These estimators are then applied to both simulated and real datasets. Numerical results show that the proposed estimators are attractive alternative to the MLE in that they are quite robust to data contamination and also highly efficient when the underlying model is true.
13 citations
TL;DR: In this paper, the authors established some new characterizations of Student's t distribution by truncated first moment, order statistics and upper record values, which can be used in the fields of probability, statistics, and other applied sciences.
Abstract: A probability distribution can be characterized through various methods. In this paper, we have established some new characterizations of folded Student’s t distribution by truncated first moment, order statistics and upper record values. It is hoped that the results will be quite useful in the fields of probability, statistics, and other applied sciences.
13 citations
TL;DR: In this article, the authors study a class of probability distributions on the positive real line, which arise by folding the classical Laplace distribution around the origin, and derive basic properties of the distribution, which include the probability density function, distribution function, quantile function, hazard rate, moments, and several related parameters.
Abstract: We study a class of probability distributions on the positive real line, which arise by folding the classical Laplace distribution around the origin. This is a two-parameter, flexible family with a sharp peak at the mode, very much in the spirit of the classical Laplace distribution. We derive basic properties of the distribution, which include the probability density function, distribution function, quantile function, hazard rate, moments, and several related parameters. Further properties related to mixture representation, Lorenz curve, mean residual life, and entropy are included as well. We also discuss parameter estimation for this new stochastic model and illustrate its potential applications with real data.
12 citations
TL;DR: A simulation study addressing the performance and robustness of a new outlier detection method proposed by Ueda (1996/2009), called Ueda’s method, and an unforeseen field of application of the method, which requires further studies was identified.
Abstract: The importance of identifying outliers in a data set is well known. Although various outlier detection methods have been proposed in order to enable reliable inferences regarding a data set, a simple but less known method has been proposed by Ueda (1996/2009). Since this new method, called Ueda’s method, has not been systematically analysed in previous research, a simulation study addressing its performance and robustness is presented. Although the method was derived assuming that the underlying data is normally distributed, its performance was analysed using data from various outlier-prone distributions commonly found in several research fields. The results obtained enable us to define the strengths and weaknesses of the method along with its limits of applicability. Furthermore, an unforeseen field of application of the method, which requires further studies was also identified.
11 citations
TL;DR: A sequential probability sampling scheme proves sufficiently apt for generating samples under the alternative hypothesis and can be justified from a theoretical point of view.
Abstract: The Rasch model allows for a conditional likelihood ratio goodness of fit test. The speed of approximation of the test statistic to the limiting distribution as a function of sample size and test length has not been analyzed so far. Three bootstrap simulation methods are analyzed with respect to their performance in providing a proper distribution of the test statistic under the null- and the alternative hypothesis. We found a stable approximation to the limiting χ
2-distribution for sample sizes of at least 500 and 10 items. The three bootstrap algorithms rendered consistent results for the H
0-cases but not for the H
1-cases. A sequential probability sampling scheme proves sufficiently apt for generating samples under the alternative hypothesis. This superiority can be justified from a theoretical point of view.
TL;DR: In this paper, a measure of spread for 3D rotation data, called the average misorientation angle, is introduced and bootstrapping is developed for this measure, which is then used in a materials science application where existing distributions do not appear to provide an adequate fit.
Abstract: While there have been recent advances in distributional theory and parametric inference for 3-D rotation data, applications still exist where it is difficult to identify an appropriate distribution for modeling. In these instances, nonparametric inference may be preferred. In this paper, a measure of spread for 3-D rotation data, called the average misorientation angle, is introduced and bootstrapping is developed for this measure. Existing parametric inference methods for estimating spread in 3-D rotations are compared to the bootstrapping procedure through a simulation study. The bootstrapping technique is then used in a materials science application where existing distributions do not appear to provide an adequate fit.
TL;DR: In this paper, the multivariate slash and skew-slash t distributions were introduced to provide alternative choices in simulating and fitting skewed and heavy tailed data and their relationship with other distributions were studied.
Abstract: In this article, we introduce the multivariate slash and skew-slash t distributions which provide alternative choices in simulating and fitting skewed and heavy tailed data. We study their relationships with other distributions and give the densities, stochastic representations, moments, marginal distributions, distributions of linear combinations and characteristic functions of the random vectors obeying these distributions. We characterize the skew t, the skew-slash normal and the skew-slash t distributions using both the hidden truncation or selective sampling model and the order statistics of the components of a bivariate normal or t variable. Density curves and contour plots are drawn to illustrate the skewness and tail behaviors. Maximum likelihood and Bayesian estimation of the parameters are discussed. The proposed distributions are compared with the skew-slash normal through simulations and applied to fit two real datasets. Our results indicated that the proposed skew-slash t fitting outperformed the skew-slash normal fitting and is a competitive candidate distribution in analyzing skewed and heavy tailed data. Mathematics Subject Classification Primary 62E10; Secondary 62P10
TL;DR: This paper uses Cox’s regression model to fit failure time data with continuous informative auxiliary variables in the presence of a validation subsample and estimates the induced relative risk function by kernel smoothing and improves the estimation by utilizing the information on the incomplete observations from non-validation subsample.
Abstract: In this paper we use Cox’s regression model to fit failure time data with continuous informative auxiliary variables in the presence of a validation subsample. We first estimate the induced relative risk function by kernel smoothing based on the validation subsample, and then improve the estimation by utilizing the information on the incomplete observations from non-validation subsample and the auxiliary observations from the primary sample. Asymptotic normality of the proposed estimator is derived. The proposed method allows one to robustly model the failure time data with an informative multivariate auxiliary covariate. Comparison of the proposed approach with several existing methods is made via simulations. Two real datasets are analyzed to illustrate the proposed method. Mathematics Subject Classification (MSC): 62G07, 62G20
TL;DR: In this article, Gosta Ekman Laboratory, Department of Psychology, Stockholm University, Stockholm, Sweden, Sweden and Arcos-Burgos Group at the John Curtin School of Medical Research, The Australian National University, Canberra, ACT, Australia.
Abstract: Author details Gosta Ekman Laboratory, Department of Psychology, Stockholm University, Stockholm, Sweden. Arcos-Burgos Group, Department of Genome Sciences, John Curtin School of Medical Research, The Australian National University, Canberra, ACT, Australia. Neuroscience Research Group, University of Antioquia, Medellin, Medellin, Colombia. Department of Civil Engineering, Faculty of Engineering, University of Porto, Porto, Portugal.
TL;DR: In this paper, the multivariate zero-truncated Charlier series (ZTCS) distribution is proposed and the associated maximum likelihood estimation method via EM algorithm is provided for analyzing correlated count data.
Abstract: Although the univariate Charlier series distribution (Biom. J. 30(8):1003–1009, 1988) and bivariate Charlier series distribution (Biom. J. 37(1):105–117, 1995; J. Appl. Stat. 30(1):63–77, 2003) can be easily generalized to the multivariate version via the method of stochastic representation (SR), the multivariate zero-truncated Charlier series (ZTCS) distribution is not available to date. The first aim of this paper is to propose the multivariate ZTCS distribution by developing its important distributional properties, and providing efficient likelihood-based inference methods via a novel data augmentation in the framework of the expectation–maximization (EM) algorithm. Since the joint marginal distribution of any r-dimensional sub-vector of the multivariate ZTCS random vector of dimension m is an r-dimensional zero-deflated Charlier series (ZDCS) distribution (1≤r
TL;DR: In this article, the characterizations of Kumaraswamy-geometric distribution introduced by Akinsete et al. (JSDA 1:1-21, 2014) are presented.
Abstract: Certain characterizations of Kumaraswamy-geometric distribution introduced by Akinsete et al. (JSDA 1:1-21, 2014) are presented.