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.
Highlights
The Weibull family of distributions has been widely used in the analysis of survival data especially in medical and engineering applications
For modelling monotone hazard rates, the Weibull distribution may be an initial choice because of its negatively and positively skewed density shapes. This distribution does not provide a reasonable parametric fit for modelling phenomenon with non-monotone failure rates such as the bathtub shaped and the unimodal failure rates which are common in reliability and biological studies
For x ≥ τ the distribution is similar to the three parameter Weibull distribution and for x < τ it is similar to the reflected Weibull distribution
Summary
The Weibull family of distributions has been widely used in the analysis of survival data especially in medical and engineering applications This family is suitable in situations where the hazard rate is constant or monotone. Many parametric families have been considered for modelling survival data with a more general shape for the hazard rate. The cumulative distribution function G(x) of the Marshall-Olkin Extended Weibull (MOEW) distribution is given by, The survival function is 1− e−xβ 1− α e−xβ. He considered a particular case where {εn} is a sequence of i.i.d. exponential random variables with mean θ(k − 1) and X0 is exponential with mean θ This model generates a first order autoregressive exponential process with mean θ and is useful in hydrological applications. K.K. Jose [7] considered various Marshall-Olkin distributions and developed autoregressive minification processes with stationary marginals as exponential, Weibull, uniform, Pareto, Gumbel etc.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
