The new reflected power function distribution: Theory, simulation &amp; application

Azam Zaka; Ahmad Saeed Akhter; Riffat Jabeen; Azam Zaka; Ahmad Saeed Akhter; Riffat Jabeen

doi:10.3934/math.2020323

AIMS Mathematics

2020, Volume 5, Issue 5: 5031-5054. doi: 10.3934/math.2020323

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Research article

The new reflected power function distribution: Theory, simulation & application

1.
College of Statistical & Actuarial Sciences, University of the Punjab, Lahore, Pakistan
2.
COMSATS University Islamabad, Lahore Campus, Lahore, Pakistan

Received: 29 April 2020 Accepted: 08 June 2020 Published: 10 June 2020
MSC : 60E05

The aim of the paper is to propose a new Reflected Power function distribution (RPFD). We provide the various properties of the new model in detail such as moments, vitality function and order statistics. We characterize the RPFD based on conditional moments (Right and Left Truncated mean) and doubly truncated mean. We also study the shape of the new distribution to be applicable in many real life situations. We estimate the parameters for the proposed RPFD by using different methods such as maximum likelihood method, modified maximum likelihood method, percentile estimator and modified percentile estimator. The aim of the study is to increase the application of the Power function distribution (PFD). Using two different data sets from real life, we conclude that the RPFD perform better as compare to different competitor models already exist in the literature. We hope that the findings of this paper will be useful for researchers in different field of applied sciences.
- characterization of truncated distribution,
- percentile estimator,
- power function distribution,
- reflected power function distribution
Citation: Azam Zaka, Ahmad Saeed Akhter, Riffat Jabeen. The new reflected power function distribution: Theory, simulation & application[J]. AIMS Mathematics, 2020, 5(5): 5031-5054. doi: 10.3934/math.2020323

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Abstract

The aim of the paper is to propose a new Reflected Power function distribution (RPFD). We provide the various properties of the new model in detail such as moments, vitality function and order statistics. We characterize the RPFD based on conditional moments (Right and Left Truncated mean) and doubly truncated mean. We also study the shape of the new distribution to be applicable in many real life situations. We estimate the parameters for the proposed RPFD by using different methods such as maximum likelihood method, modified maximum likelihood method, percentile estimator and modified percentile estimator. The aim of the study is to increase the application of the Power function distribution (PFD). Using two different data sets from real life, we conclude that the RPFD perform better as compare to different competitor models already exist in the literature. We hope that the findings of this paper will be useful for researchers in different field of applied sciences.

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