Journal of Iranian Statistical Society
Volume:15 Issue: 1, 2016

In this paper, we propose an approach for the nonparametric estimation of the conditional survival function of a time to failureý ýgiven a time-varying covariate under interval-censoring for the failure time. Our strategy consists iný ýmodeling the covariate path with a random effects model, ýas is done in the degradation and joint longitudinal and survival data modelingý ýliterature, ýthen in using a nonparametric estimator of the conditional survival function for time-fixed covariate. ýWe derive the large sample bias and variance of the estimator under simplifying assumptions and we investigateý ýits finite sample efficiency and robustness by simulation. ýWe show how the proposed method can be useful iný ýthe early stages of data exploration and model specification by applying it to two real datasets, ýone oný ýthe time to infestation of trees by pine weevil and one on the reliability of a piece of electrical equipment. ýWe conclude by suggesting avenues to make this data exploration method more suitable for formal inferencesý.

In this paper, ýwe propose new residuals for gamma regression models, ýassuming that both mean and shape parameters follow regression structures. The models are summarized and fitted by applying both classic and Bayesian methods as proposed by Cepeda-Cuervo (2001). The residuals are proposed from properties of the biparametric exponential family of distributions. ýSimulated and real data setsý ýare analyzed to determine the performance and behavior of the proposed residuals.

In this paper, we discuss the usual stochasticý, ýlikelihood ratio, ýdispersive and convex transform order between two parallel systems with independent heterogeneous extended generalized exponential components. ýWe also establish the usual stochastic order between series systems from two independent heterogeneous extended generalized exponential samples. ýFinally, ýwe find lower and upper bounds for the Renyi entropy and cumulative residual entropy of series and parallel systemsý.

Let T1,...,Tn be exchangeable random variables and suppose that T{1:n} represents the ith order statistic among Tis, i=1,...,n. ýIn this paper some expressions for the joint distribution ýof (T{1:n},...,T{n:n}), ýmarginal distribution of T{1:n} and the joint distribution of (T{r:n},T{k:n}), 1≤ r ≤ k ≤n ýin terms of the joint distribution (or joint reliability) function of Ti's are provided. ýUsing these and when {T1,...,Tn} is a sequence ofý ýlifetimes, some expressions for the mean residual life functions of a n-kout-of-n systemý, Hnk(t)=E(T{k:n}-t|T{1:n}>t) and Mn{r,k}(t)=E(T{k:n}-t|T{r:n}>t), ý1≤ r≤ k≤ n in terms of the joint survival function of Ti's are givený. ýAlso, ýsome examples are providedý.

This article derives the distribution of random matrix X associated with the transformation Y = X*X, such that Y has a Riesz distribution for real normed division algebras. Two versions of this distributions are proposed and some of their properties are studied.

In this paper, we introduce a new five-parameter distribution with increasing, decreasing, bathtub-shaped failure rate called the Beta-Weibull-Logarithmic (BWL) distribution. Using the Sterling Polynomials, various properties of the new distribution such as its probability density function, its reliability and failure rate functions, quantiles and moments, R$acute{e}$nyi and Shannon entropies, moments of order statistics, Bonferroni and Lorenz curves were derived. then the maximum likelihood estimation of BWL distribution for the parameters of BWL distribution are found. Finally the usefulness of this distribution for real data are presented.