The Sine Modified Lindley Distribution

Lishamol Tomy,Veena G,Christophe Chesneau

doi:10.3390/mca26040081

Lishamol Tomy, Veena G + Show 1 more

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https://doi.org/10.3390/mca26040081

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Abstract

The paper contributes majorly in the development of a flexible trigonometric extension of the well-known modified Lindley distribution. More precisely, we use features from the sine generalized family of distributions to create an original one-parameter survival distribution, called the sine modified Lindley distribution. As the main motivational fact, it provides an attractive alternative to the Lindley and modified Lindley distributions; it may be better able to model lifetime phenomena presenting data of leptokurtic nature. In the first part of the paper, we introduce it conceptually and discuss its key characteristics, such as functional, reliability, and moment analysis. Then, an applied study is conducted. The usefulness, applicability, and agility of the sine modified Lindley distribution are illustrated through a detailed study using simulation. Two real data sets from the engineering and climate sectors are analyzed. As a result, the sine modified Lindley model is proven to have a superior match to important models, such as the Lindley, modified Lindley, sine exponential, and sine Lindley models, based on goodness-of-fit criteria of importance.

Highlights

The last few years in applied sciences have been marked by the need and volume of data to be analyzed
The sine modified Lindley model is proven to have a superior match to important models, such as the Lindley, modified Lindley, sine exponential, and sine Lindley models, based on goodness-of-fit criteria of importance
The data are presented briefly, accompanied with their reference; A table that encapsulates the basic statistical measures of the data is provided; The goodness-of-fit measures of the models under consideration are evaluated and arranged in order of model performance in a table; The maximum likelihood estimate (MLE)(s) of the model parameters is(are) shown, as well as the relevant standard error (SE), as supplementary work; It is concluded with a visual concept by presenting the histogram of the data and the epdf, as well as the empirical cdf plots and ecdf for the S-modified Lindley (ML) model exclusively in another graph

Summary

Introduction

The last few years in applied sciences have been marked by the need and volume of data to be analyzed To meet this need, new models have been proposed, and their improvement is a hot topic. New models have been proposed, and their improvement is a hot topic These require, among other things, the underlying development of new (statistical or probabilistic) distributions. The families described by ”trigonometric transformations" have gained a lot of interest because of their applicability and working capability in a variety of situations. The cumulative distribution function (cdf) and probability density function (pdf) are given by hπ i

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