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G Families of Probability Distributions - Theory and Practices (Hardcover)
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G Families of Probability Distributions - Theory and Practices (Hardcover)
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Statistical distributions are important tools to model the
characteristics of data sets such as right or left skewness,
bi-modality or multi-modality observed in different applied
sciences such as engineering, medicine, and finance, among others.
The well-known distributions such as normal, Weibull, gamma,
Lindley are extensively used because of their simple forms and
identifiability properties. However, mostly in the last decade or
so, researchers have focused on the more complex and flexible
distributions, referred to as Generalized or simply G families of
distributions to increase the modeling ability of these
distributions by adding one or more shape parameters. The main aim
of this edited book is to present new development currently made by
various researchers in the field of G families of contributions
distributions. The book will help future and current researchers in
the field of this research. Some of the objectives are listed
below: Develop new univariate continuous and discrete G families of
probability distributions. Develop new bivariate continuous and
discrete G families of probability distributions. Derive useful
mathematical properties such as, ordinary and incomplete moments,
moments generating functions, residual life and reversed residual
life functions, order statistics, quantile spread ordering and
entropies, among others and some bivariate and multivariate
extensions of the new and existing models using a simple type
copula such as: Farlie Gumbel Morgenstern copula. Modified Farlie
Gumbel Morgenstern copula. Clayton copula. Renyi entropy copula.
Ali-Mikhail-Haq copula. haracterize the models via several
techniques such as: the conditional expectation. the truncated
moment. the hazard functions. Mills ratio. certain functions of the
random variable. the 1st order statistic. the conditional
expectation of the record values. Assess the performance of the
used estimation methods via Monte-Carlo simulation studies. Show
the wide importance and the flexibility of the new models against
the competitive models. Construct some new regression models based
on the new proposed G families and use in statistical prediction.
Application of many new useful goodness-of-fit tests for right
censored validation such as the Nikulin-Rao-Robson goodness-of-fit
test, modified Nikulin-Rao-Robson goodness-of-fit test,
Bagdonavicius-Nikulin goodness-of-fit test and modified
Bagdonavicius-Nikulin goodness-of-fit test to the new families.
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