The Quantile Based Flattened Logistic Distribution: Some properties and Application

TL;DR

This paper investigates the properties of the quantile based flattened logistic distribution, deriving key statistical measures, estimating its parameters using L-moments, and applying it to real data with goodness of fit tests.

Contribution

It provides a comprehensive study of the distribution's properties, closed-form L-moments, parameter estimation methods, and real data application.

Findings

Derived closed-form L-moments and L-ratios.

Estimated parameters using L-moments matching.

Validated model with real data and goodness of fit tests.

Abstract

In this paper, the quantile based flattened logistic distribution introduced by Gilchrist has been studied. Some classical and quantile based properties of the distribution have been obtained. Closed form expression of L-moments and L-ratios of the distribution have been obtained. A quantile based analysis based on the methods of matching L-moments estimation is employed to estimate the parameters of the proposed model. We further derive the asymptotic variance-covariance matrix of the L-Moments estimator of the proposed model. Finally, we apply the proposed model to a real data set and perform some goodness of fit tests.