A New Generalized Modified Weibull Distribution

Abstract

We introduce a new distribution, so called A new generalized modified Weibull (NGMW) distribution. Various structural properties of the distribution are obtained in terms of Meijer's $G$--function, such as moments, moment generating function, conditional moments, mean deviations, order statistics and maximum likelihood estimators. The distribution exhibits a wide range of shapes with varying skewness and assumes all possible forms of hazard rate function. The NGMW distribution along with other distributions are fitted to two sets of data, arising in hydrology and in reliability. It is shown that the proposed distribution has a superior performance among the compared distributions as evidenced via goodness--of--fit tests

The Weibull Distribution: Reliability Characterization Based on Linear and Circular Consecutive Systems

“…When the pair of components [j, j + 1] fails for any j = 1, 2, 3, 4 then both the linear and circular consecutive 2 − out − of − 5 : F system fail. However, if only the components [5,2] fail then the circular 2 − out − of − 5 : F system fails but the corresponding linear 2 − out − of − 5 : F system continues to function. Therefore, for a given k and n, the circular consecutive k − out − of − n : F system has generally greater failure possibilities than that of the corresponding linear consecutive k − out − of − n : F system and thus less reliability.…”

Discrete Inverted Nadarajah-Haghighi Distribution: Properties and Classical Estimation with Application to Complete and Censored data

“…In many fields, including medical science, engineering science, economics, and other allied sciences, there is a great emphasis on modelling through continuous lifetime distributions [1,2,3,4]. The discretization phenomenon generally arises when it becomes impossible or inconvenient to measure the life length of a product or device on a continuous scale.…”