Alpha Logarithm Transformed Half Logistic Distribution: Properties and Applications

Abstract

In this paper, we introduce a new two parameter Alpha Logarithm Transformed Half Logistic (ALTHL) distribution. A new method has been proposed to introduce an extra parameter to a family of distributions for more flexibility .The proposed family may be named as Alpha Logarithm Transformed Half Logistic. This can be obtained via reparameterizing the exponentiated Kumaraswamy G-logarithmic family and the alpha logarithmic family of distributions. The recommended distribution reveals increasing, decreasing and bath-shaped probability Density, Distribution and Hazard rate function and Survival function. Some distributional properties of new model are investigated which include the Density Function, Distribution Function (DF), Quantile Function(QF), Moments, Moment Generating Function (MGF), Cumulative Generating Function (CGF).

Introduction

I. INTRODUCTION

In statistical literature a good measure of work has been dedicated to Half Logistic distribution. Several authors and the references cited therein have carried out extensive studies as relate to the estimation, prediction and several other inferences with respect to Half Logistic distribution. The reliability function of Half Logistic distribution decreases at a large amount higher rate than the reliability function of exponential distribution.

To pick up the characteristics of these traditional distributions, researchers have been raising various extensions and modified forms of these distributions. However, in the recent literature, researchers have shown a deep interest in proposing new families of distributions. The literature is packed with such methods that are quite prosperous and still growing quickly.

A  α Logarithmic Transformed Family of Distributions with Application introduced Sunku Dey et al (2017). A Flexible Reduced Logarithmic-X Family of Distributions with Biomedical Analysis. A Flexible Reduced Logarithmic-X Family of Distributions with Biomedical analysis introduced YinglinLiu et al (2020). Vijaya  lakshmi and Anjaneyulu (2018) studied The Odd Generalized Exponential Type-I Generalized Half Logistic Distribution: Properties and Application. Vijaya Lakshmi and Anjaneyulu (2019) studied Quadratic Rank Transmuted Half Logistic Lomax Distribution: Properties and Application. Vijaya Lakshmi and Anjaneyulu (2019) studied Half Logistic Pareto Distribution: Properties and Application.  Laba Handique et al (2020) studied the New Extended Burr-III Distribution: Its Properties and Applications. Mi Zichun et al (2020) studied A New Extended X-family of distribution: Properties and Applications.

Major  inspiration  behind  the  proposed  family  is  to  find  an  expansion  of  the  Half  Logistic  distribution  with   one  addit ional  parameters  to  bring  in  more  flexibility  with  respect to skewness, kurtosis, tail weight and length. 

This encompasses number known distributions as special and connected cases, also to ensure that it provides better alternative in the data modeling not only to its sub models including the Half Logistic distribution, but to other recent extensions.

The chapter is organized as follows. The new distribution Alpha Logarithm Transformed Half Logistic (ALTHL) is developed in the above. A comprehensive account of statistical properties of the new distribution is provided in Section 2. In section 3.1, 3.2 and 3.3 we discuss the Moments, Moment Generating Function and Cumulative Generating Function for ALTHL distribution. Sequentially, Section 4 applied the real life data sets the time-to-event data from different basketball matches and these matches were played during the period 1986– 2021 and the survival times of the patients affected the Leukemia at the final stage on ALTHL for checking the behavior of new distribution.

References

[1] Abinash, M.J, Vasudevan, V. A (2018), A study on wrapper-based feature selection algorithm for leukemia dataset, Intelligent Engineering Informatics, 695, pp: 311-321. [2] Laba Handique , Rana Muhammad Usman and Subrata Chakraborty (2020), New Extended Burr-III Distribution: Its Properties and Applications, Thailand Statistician, 18(3), pp: 267-280 [3] Mi Zichuan, Saddam Hussain, Anum Iftikhar, Muhammad Ilyas, Zubair Ahmad, Dost Muhammad Khan,and Sadaf Manzoor (2020). A New Extended X-family of distribution: Properties and Applications, Computational and Mathematical Methods in Medicine, pp:1-13. [4] Sanku Dey , Mazen Nassar and Devendra Kumar (2017), ? Logarithmic Transformed Family of Distributions with Application, Annals of Data Science, 4(4), pp: 457–482. [5] Vijaya Lakshmi, M. and Anjaneyulu, G. V. S. R. (2018). The Odd Generalized Exponential Type-I Generalized Half Logistic Distribution: Properties and Application, International Journal of Engineering and Computer Science (IJECS), 7, 1, PP. 23505-23516. [6] Vijaya Lakshmi, M. and Anjaneyulu, G. V. S. R. (2019), “Quadratic Rank Transmuted Half Logistic Lomax Distribution: Properties and Application”, International Journal in IT & Engineering (IJITE), 7(6), pp. 1-12. [7] Vijaya Lakshmi, M. and Anjaneyulu, G. V. S. R. (2020), Half Logistic - Pareto Distribution: Properties and Application, International Journal in IT & Engineering (IJITE), 7(6), pp. 1-12 [8] YinglinLiu, MuhammadIlyas, SaimaK.Khosa, EisaMuhmoudi, ZubairAhmad, Dost Muhammad Khan and Hamedani, G. G. (2020), A Flexible Reduced Logarithmic-X Family of Distributions with Biomedical Analysis,Vol.2020, pp:1-15.

Copyright

Copyright © 2023 I. Narasimha Rao, M. Vijaya Lakshmi, G. V. S. R Anjaneyulu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.