Abstract
We propose a distribution called Odds Exponential Log Logistic Distribution (OELLD), which is an odds family of distribution. Its hazard rate is an increasing and decreasing function based on the value of the parameter. Explicit expressions for the ordinary moments, L-moments, quantile, generating functions, Bonferroni Curve, Lorenz Curve, Gini's index and order statistics are derived. The parameters of the proposed distribution are estimated by using maximum likelihood method and also illustrated by a lifetime data set.
Highlights
In describing the real world phenomena, the distributions are very much useful
Proportional Odds Model (POM), Proportional Hazard Model (PHM), Proportional reversed hazard model (PRHM), Power Transformed Model (PTM) are some of the models originated from this idea to add a shape parameter
The statistics W* and A* are listed in this Table 1 for the models. It can be seen from the table given below, the proposed Odds Exponential Log Logistic Distribution (OELLD) has the smallest values for the statistics W* and A* than most of the other models, that is, the proposed model fits the breaking stress of carbon fibres data better than most of the other models considered
Summary
In describing the real world phenomena, the distributions are very much useful. In spite of the fact that a number of distributions are developed, always there is a scope for introducing distributions, analysing their properties to use them for fitting real world scenarios. New distributions are defined by introducing one or more parameters to the distribution functions. The addition of parameters to the distribution functions makes the distribution richer and more flexible for modelling life time data.
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