Some Generalizations of Weibull Distribution and Related Processes

Abstract

A new class of distributions containing Marshall-Olkin extended Weibull distribution is introduced. The role of this distribution in the study of minification process is established. A new class of distributions that includes the Laplace and Logistic distributions is introduced. Properties and generation of Marshall-Olkin extended Double Weibull distribution and Marshall-Olkin extended asymmetric double Weibull distribution are discussed. The distribution of daily stock price index of Bombay stock exchange (INDIA) is identified as generalised asymmetric double Weibull model and its estimation and predictions are done.

A Stationary Proportional Hazard Class Process and its Applications

“…It is observed in both the cases that the data are coming from a positive valued lag-1 stationary process and there are several instances for which X n = X n+1 , which cannot be ignored. It may be mentioned that there are several positive valued lag-1 stationary processes available in the literature; for example the exponential process by Tavares [27], Weibull and gamma process by Sim [26], Pareto process by Yeh et al [28], semi-Pareto process by Pillai [24] and Arnold and Hallet [3], Weibull process by Jayakumar and Girish Babu [14], and see the references cited there in. Unfortunately, none of these processes can be applied in this case as in all these cases P (X n = X n+1 ) = 0.…”

Stationary GE-Process and its Application in Analyzing Gold Price Data

“…Due to this reason, several non-Gaussian processes have been introduced and studied quite extensively in the literature. For example, stationary exponential process by Tavares [20], Weibull and gamma processes by Sim [19] Logistic process by Arnold [2], Pareto process by Arnold and Hallet [4], see also Arnold [3], semi-Pareto process by Pillai [18], Marshall-Olkin bivariate Weibull processes by Jose, Ristić and Joseph [11], generalized Weibull process by Jayakumar and Girish Babu [10] and see the references cited therein. In all these cases the emphasis is to develop a stationary process which has specific marginals.…”