Kumaraswamy Generalized Power Lomax Distributionand Its Applications

Abstract

In this paper, a new five-parameter distribution is proposed using the functionalities of the Kumaraswamy generalized family of distributions and the features of the power Lomax distribution. It is named as Kumaraswamy generalized power Lomax distribution. In a first approach, we derive its main probability and reliability functions, with a visualization of its modeling behavior by considering different parameter combinations. As prime quality, the corresponding hazard rate function is very flexible; it possesses decreasing, increasing and inverted (upside-down) bathtub shapes. Also, decreasing-increasing-decreasing shapes are nicely observed. Some important characteristics of the Kumaraswamy generalized power Lomax distribution are derived, including moments, entropy measures and order statistics. The second approach is statistical. The maximum likelihood estimates of the parameters are described and a brief simulation study shows their effectiveness. Two real data sets are taken to show how the proposed distribution can be applied concretely; parameter estimates are obtained and fitting comparisons are performed with other well-established Lomax based distributions. The Kumaraswamy generalized power Lomax distribution turns out to be best by capturing fine details in the structure of the data considered.

Harris Extended Power Lomax Distribution: Properties, Inference and Applications

“…) by Nagarjuna, V. B. V. (2021), Kumaraswamy Generalized Lomax ( ) distribution by Shams, T. M. (2013). Tables 3, 4 provide the estimated value of the parameters for data set 1 and 2 respectively.…”

A New Extension of the Kumaraswamy Exponential Model with Modeling of Food Chain Data

“…The new suggested model (KMKE model) Food chain data New K-Weibull model Failure times data [50] K-generalized Rayleigh model Engineering data [51] K-modified Weibull model Failure times data [52] K-transmuted exponentiated modified Weibull model Medical data [53] K-transmuted modified Weibull model Failure times data [54] K-Gompertz Makeham model Physics data [55] K-Gumbel model Engineering data [56] K-generalized gamma model Industrial and medical data [57] K-generalized power Lomax model Physics data [58] K-Burr XII model Engineering, physics and medical data [59] K-generalized inverse Lomax model Reliability and survival data [60] K-Dagum model Income and lifetime data [61] Modified K model Engineering data [62] Transmuted K-Lindley model Medical data [63] K-Marshall-Olkin exponential model Medical data [64] K-half logistic model Physics and medical data [65] K-log logistic model Medical data [66] K-Marshall-Olkin log-logistic model Physics data [67] Modified K Weibull model Reliability and engineering data [68] K-inverted Topp-Leone model COVID-19 data [69] Kavya-Manoharan-K model COVID-19 and physics data [70] Transmuted K model Medical and environmental data [71] Table 1. Cont.…”

On the Accuracy of the Sine Power Lomax Model for Data Fitting

“…The data correspond to times in days between 109 successive mining catastrophes in Great Britain, for the period 1875-1951, as published in [47]. The sorted data are given as follows: 1,4,4,7,11,13,15,15,17,18,19,19,20,20,22,23,28,29,31,32,36,37,47,48,49,50,54,54,55,59,59,61,61,66,72,72,75,78,78,81,93,96,99,108,113,114,120,120,120,123,124,129,131,137,145,…”

“…The practical gain is particularly impressive; the PL model is better than ten competing models for analyzing the bladder cancer patients dataset of [8], all based on the Lomax model. For the sake of optimality, some motivated distributions extending or generalizing the PL distribution was introduced, including the type II Topp-Leone PL (TIITLPL) distribution by [27], type I half logistic PL distribution by [28], inverse PL distribution by [29], Marshall-Olkin PL distribution by [30], exponentiated PL distribution by [31] and Kumaraswamy generalized PL distribution (KPL) by [32]. The main strategy of these proposed distributions is to add more parameters to the PL distribution based on exponentiated, transmuted or truncated schemes.…”