Generalized Mixtures of Gamma and Exponentials and Reliability Properties of the Maximum from Friday and Patil Bivariate Exponential Model

The minimum and maximum order statistics from many of the common bivariate exponential distributions are predominantly generalized mixtures of exponentials; however, the maximum from the Friday and Patil bivariate exponential (FPBVE) model is either a generalized mixture of three or fewer exponentials or a generalized mixture of gamma and exponentials. In this article, we obtain conditions based on the weights and parameters of the generalized mixtures of gamma and one or two exponential distributions that yield legitimate probability models. Furthermore, we analyze properties of the failure rate of the maximum from the FPBVE model. This answers a question raised in Baggs and Nagaraja (1996 Baggs , G. E. , Nagaraja , H. N. ( 1996 ). Reliability properties of order statistics from bivariate exponential distributions . Commun. Statist. Stochastic Mod. 12 : 611 – 631 .[Taylor & Francis Online] , [Google Scholar]).     

A Robust Procedure in Nonlinear Models for Repeated Measurements

Nonlinear regression models arise when definite information is available about the form of the relationship between the response and predictor variables. Such information might involve direct knowledge of the actual form of the true model or might be represented by a set of differential equations that the model must satisfy. We develop M-procedures for estimating parameters and testing hypotheses of interest about these parameters in nonlinear regression models for repeated measurement data. Under regularity conditions, the asymptotic properties of the M-procedures are presented, including the uniform linearity, normality and consistency. The computation of the M-estimators of the model parameters is performed with iterative procedures, similar to Newton–Raphson and Fisher's scoring methods. The methodology is illustrated by using a multivariate logistic regression model with real data, along with a simulation study.     

The 3 F 2 with Complex Parameters as Generating Function of Discrete Distribution

A new discrete family of probability distributions that are generated by the ₃ F ₂ function with complex parameters is presented. Some of the properties of this new family are studied as well as methods of estimation for its parameters. It affords considerable flexibility of shape which turns the distribution into an appropriate candidate for modeling data that cannot be adequately fitted by classical families with fewer parameters. Finally, three examples in the fields of Agriculture and Education are included in order to show the versatility and utility of this distribution.     

Stochastic Aging Classes for the Maximum Statistic from Friday and Patil Bivariate Exponential Distribution Family

Friday and Patil bivariate exponential (FPBVE) distribution family is one of the most flexible bivariate exponential distributions in the literature; among others, it contains the bivariate exponential models due to Freund, Marshall–Olkin, Block–Basu, and Proschan–Sullo as particular cases. In this article, we discuss the stochastic aging of the maximum statistic from FPBVE model in according to the log-concavity of its density function, i.e., in the increasing or decreasing likelihood ratio classes (ILR or DLR), and consequently in the IFR and DFR classes. Furthermore, a kind of DFR distributions which are not DLR is derived from our classification.     

Identifying Preferences for Conditional Cooperation Using Individual Beliefs

The relationship between contributions and elicited beliefs in a repeated two-person public good experiment is modeled with the help of a parsimounious random-utility function that allows for conditionally cooperative, opportunistic, and altruistic patterns of behavior. Under standard assumptions, a latent-class mixed logit specification with three sub-populations is shown to capture well heterogeneity in individual contribution levels over time, while also accomodating for different degrees of heteroscedasticity. The estimation results are consistent with the conjecture that the majority of players in public goods games are strongly conditional cooperators, with smaller fractions of the population leaning to opportunistic or altruistic behavior.     

A Note on Simultaneous Confidence Intervals for Ratio of Variances

An explicit formula for confidence intervals for ratios of variances of several populations is presented. The intervals are based on jackknife statistics and the critical point of the studentized range distribution. The asymptotic probability of coverage is not less than the nominal value provided that the distributions of the sampled populations belong to a location-scale family of probabilities with finite fourth moment.     

A-optimal designs for heteroscedastic multifactor regression models

Abstract

This paper searches for A-optimal designs for Kronecker product and additive regression models when the errors are heteroscedastic. Sufficient conditions are given so that A-optimal designs for the multifactor models can be built from A-optimal designs for their sub-models with a single factor. The results of an efficiency study carried out to check the adequacy of the products of optimal designs for uni-factor marginal models when these are used to estimate different multi-factor models are also reported.     

The Poisson-conjugate Lindley mixture distribution

ABSTRACT

A new discrete distribution that depends on two parameters is introduced in this article. From this new distribution the geometric distribution is obtained as a special case. After analyzing some of its properties such as moments and unimodality, recurrences for the probability mass function and differential equations for its probability generating function are derived. In addition to this, parameters are estimated by maximum likelihood estimation numerically maximizing the log-likelihood function. Expected frequencies are calculated for different sets of data to prove the versatility of this discrete model.