Various characterizations of the Weibull Geometric distribution are presented. These characterizations are based, on a simple relationship between two truncated moments ; on hazard function ; and on functions of order statistics.

In this paper a method for the parameter estimation of a Weibull distribution is explained. It is based on the estimates of the cumulative probability function performed by a wavelet method. The estimates, obtained by the application of the proposed method, are compared with the results based on other literature estimators. In particular, it is shown that the estimates are stable also when samp...

Control charts are widely used for process monitoring. Software reliability process can be monitored efficiently by using Statistical Process Control (SPC). It assists the software development team to identify failures and actions to be taken during software failure process and hence, assures better software reliability. In this paper we propose a control mechanism based on the cumulative quant...

In this paper, we develop the length-biased form of the weighted Weibull distribution (WWD) named as length-biased weighted Weibull distribution (LBWWD). Well known distributions are generated by expanding suitable function of the parameters. Shape of the distribution is studied in detail. Various properties of length-biased WWD are discussed. Newby’s method along with method of moment has been...

The cumulative distribution function (CDF) of the T-X family is given by R{W(F(x))}, where R is the CDF of a random variable T, F is the CDF of X and W is an increasing function defined on [0, 1] having the support of T as its range. This family provides a new method of generating univariate distributions. Different choices of the R, F and W functions naturally lead to different families of dis...

Abstract Statistical inferences of the parameters included in a competing risks model are presented. It is assumed here that the causes of failures may occur at times that follow modified Weibull distributions. The case of Weibull distributions can be derived as special case of the problem studied in this paper. The maximum likelihood procedure is used to get the point estimations and asymptoti...

We derive a closed form solution for the Kullback-Leibler divergence between two Weibull distributions. These notes are meant as reference material and intended to provide a guided tour towards a result that is often mentioned but seldom made explicit in the literature. 1 The Weibull Distribution TheWeibull distribution is the type III extreme value distribution; its probability density functio...

This paper presents a new approach for the determination of the wind speed distribution based on wind speed data. This approach is based on the fact that, in general, wind speed distributions restricted to seasons of year or months are different. Therefore, instead of one Weibull density function, a convex combination of Weibull density functions is considered for a calendar year. This model im...

A generalization of the exponentiated Weibull geometric model called the transmuted exponentiated Weibull geometric distribution is proposed and studied. It includes as special cases at least ten models. Some of its structural properties including order statistics, explicit expressions for the ordinary and incomplete moments and generating function are derived. The estimation of the model param...

A generalization of the exponentiated modified Weibull distribution so-called the transmuted exponentiated modified Weibull distribution is proposed and studied. Various structural properties including explicit expressions for the moments, quantiles, and moment generating function of the new distribution are derived. The estimation of the model parameters is performed by least square method. We...