The Kumaraswamy GEV distribution

The popular generalized extreme value (GEV) distribution has not been a flexible model for extreme values in many areas. We propose a generalization – referred to as the Kumaraswamy GEV distribution – and provide a comprehensive treatment of its mathematical properties. We estimate its parameters by the method of maximum likelihood and provide the observed information matrix. An application to some real data illustrates flexibility of the new model. Finally, some bivariate generalizations of the model are proposed.     

Decision-making for paired comparison using the extended amended Davidson model

For decision purpose, one of the commonly used statistical applications is the comparison of two or more objects or characteristics. Sometimes, it is not possible to compare the objects at a time or when the number of objects under study is large and the differences between the objects become small, then a useful way is to compare them in pairwise manner. Because of its practical nature, the fields in which paired comparison techniques are being used are numerous. Many Bayesian statisticians have focused their attention on the practical and usable paired comparison technique and have successfully performed the Bayesian study of many of the paired comparison models. In the current study, analysis of the amended Davidson model (ADM) which has been extended after incorporating the order effect parameter is narrated. For this intention, both the informative and non informative priors are used. The said model is studied for the case of four treatments which are compared pairwise.     

Pollutant Ground Concentrations of Nonneutrally Buoyant Particles

A methodology is suggested for the estimation of the mass density and the cumulative ground deposition of a nonvolatile, nonneutrally buoyant, air pollutant (liquid or solid) released from a polluted column (following an explosion caused during routine operation in, e.g., the chemical industry or due to any kind of hostile act) and deposited on the ground via gravitational settling. In many cases, the deposited mass due to gravitational settling constitutes a significant fraction of the original inventory released from the source. Implementation of the methodology in preliminary risk assessments can serve as an efficient tool for emergency planning for both immediate and long‐term measures such as evacuation and decontamination. The methodology considers, inter alia, an estimation of the critical particle diameter, particle size, and mass distributions along the polluted column. This methodology was developed to apply in rural regions since proper application of relevant meteorological input data can be accomplished mainly for such areas.     

The Kumaraswamy skew-t distribution and its related properties

Skew normal distribution is an alternative distribution to the normal distribution to accommodate asymmetry. Since then extensive studies have been done on applying Azzalini’s skewness mechanism to other well-known distributions, such as skew-t distribution, which is more flexible and can better accommodate long tailed data than the skew normal one. The Kumaraswamy generalized distribution (Kw ? F) is another new class of distribution which is capable of fitting skewed data that can not be fitted well by existing distributions. Such a distribution has been widely studied and various versions of generalization of this distribution family have been introduced. In this article, we introduce a new generalization of the skew-t distribution based on the Kumaraswamy generalized distribution. The new class of distribution, which we call the Kumaraswamy skew-t (KwST) has the ability of fitting skewed, long, and heavy-tailed data and is more flexible than the skew-t distribution as it contains the skew-t distribution as a special case. Related properties of this distribution family such as mathematical properties, moments, and order statistics are discussed. The proposed distribution is applied to a real dataset to illustrate the estimation procedure.     

Multiple comparisons of exponential location parameters with a control based on doubly censored sample under heteroscedasticity

In this article, a one-sample procedure for multiple comparisons of exponential location parameters with a control under heteroscedasticity is proposed. The observations are obtained by doubly censored samples. A one-sided and two-sided confidence intervals are used to perform such multiple comparisons. Statistical tables of critical values and an example of comparing four drugs in treating leukemia are provided.     

A revisit to test the equality of variances of several populations

We revisit the problem of testing homoscedasticity (or, equality of variances) of several normal populations which has applications in many statistical analyses, including design of experiments. The standard text books and widely used statistical packages propose a few popular tests including Bartlett's test, Levene's test and a few adjustments of the latter. Apparently, the popularity of these tests have been based on limited simulation study carried out a few decades ago. The traditional tests, including the classical likelihood ratio test (LRT), are asymptotic in nature, and hence do not perform well for small sample sizes. In this paper we propose a simple parametric bootstrap (PB) modification of the LRT, and compare it against the other popular tests as well as their PB versions in terms of size and power. Our comprehensive simulation study bursts some popularly held myths about the commonly used tests and sheds some new light on this important problem. Though most popular statistical software/packages suggest using Bartlette's test, Levene's test, or modified Levene's test among a few others, our extensive simulation study, carried out under both the normal model as well as several non-normal models clearly shows that a PB version of the modified Levene's test (which does not use the F-distribution cut-off point as its critical value), and Loh's exact test are the “best” performers in terms of overall size as well as power.     

A general approximation to quantiles

For many continuous distributions, a closed-form expression for their quantiles does not exist. Numerical approximations for their quantiles are developed on a distribution-by-distribution basis. This work develops a general approximation for quantiles using the Taylor expansion. Our method only requires that the distribution has a continuous probability density function and its derivatives can be derived to a certain order (usually 3 or 4). We demonstrate our unified approach by approximating the quantiles of the normal, exponential, and chi-square distributions. The approximation works well for these distributions.     

The Condom Fairy program: A novel mail-order service for condoms and sexual health supplies

Abstract

Objective: In recent years college health professionals have used a variety of innovative strategies to increase availability and accessibility of condoms and safer sex products. The purpose of this study is to evaluate the efficacy and efficiency of a mail-order delivery program titled the Condom Fairy. Participants: Seven hundred thirty-three students (63.4% women, 86.1% heterosexual, and 59.2% Caucasian) completed a questionnaire assessing their overall experience with the program. Methods: Participants completed a 60 item questionnaire 30?days after receiving condoms and safer sex products. Results: Overall, 46,980 condoms were distributed over a six semester period. Almost all of the participants (97.4%) reported they ordered male condoms while 58.0% ordered sexual lubricant, 11.1% female condoms, and 10.2% latex dams. Nearly than three-quarters (73.9%) of participants reported they used the condoms provided. Conclusions: Findings support the implementation of innovative mail-in condom and safer sex product programs on college campuses.     

Inverse gaussian accelerated test models based on cumulative damage

The failure of a system under environmental stress often can be described by an accelerated test model which incorporates the environmental variable L. Here, the failure of such a system at environmental level L is modeled as the first passage of accumulated damage to a critical threshold value. Assuming a discrete additive damage model leads to a Birnbaum–Saunders-type distribution for the failure time which can be closely approximated by an inverse Gaussian-type model. However, if a continuous damage model based on a Gaussian process is assumed, a more general family of inverse Gaussian accelerated test models is obtained. Three sets of failure data are discussed to illustrate the usefulness of this general family.     

A non-iterative posterior sampling algorithm for linear quantile regression model

In this article, a non-iterative posterior sampling algorithm for linear quantile regression model based on the asymmetric Laplace distribution is proposed. The algorithm combines the inverse Bayes formulae, sampling/importance resampling, and the expectation maximization algorithm to obtain independently and identically distributed samples approximately from the observed posterior distribution, which eliminates the convergence problems in the iterative Gibbs sampling and overcomes the difficulty in evaluating the standard deviance in the EM algorithm. The numeric results in simulations and application to the classical Engel data show that the non-iterative sampling algorithm is more effective than the Gibbs sampling and EM algorithm.