Topp-Leone Lomax Distribution

A new three-parameter continuous model called the exponentiated half-logistic Lomax distribution is introduced in this paper. Basic mathematical properties for the proposed model were investigated which include raw and incomplete moments, skewness, kurtosis, generating functions, Rényi entropy, Lorenz, Bonferroni and Zenga curves, probability weighted moment, stress strength model, order statistics, and record statistics. The model parameters were estimated by using the maximum likelihood criterion and the behaviours of these estimates were examined by conducting a simulation study. The applicability of the new model is illustrated by applying it on a real data set.

Download Full-text

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

Modelling ◽

10.3390/modelling2010005 ◽

2021 ◽

Vol 2 (1) ◽

pp. 78-104

Author(s):

Vasili B. V. Nagarjuna ◽

R. Vishnu Vardhan ◽

Christophe Chesneau

Keyword(s):

Statistical Model ◽

Simulation Study ◽

Statistical Models ◽

Goodness Of Fit ◽

Data Fitting ◽

Applied Science ◽

Survival Distribution ◽

Lomax Distribution ◽

Model Based

Every day, new data must be analysed as well as possible in all areas of applied science, which requires the development of attractive statistical models, that is to say adapted to the context, easy to use and efficient. In this article, we innovate in this direction by proposing a new statistical model based on the functionalities of the sinusoidal transformation and power Lomax distribution. We thus introduce a new three-parameter survival distribution called sine power Lomax distribution. In a first approach, we present it theoretically and provide some of its significant properties. Then the practicality, utility and flexibility of the sine power Lomax model are demonstrated through a comprehensive simulation study, and the analysis of nine real datasets mainly from medicine and engineering. Based on relevant goodness of fit criteria, it is shown that the sine power Lomax model has a better fit to some of the existing Lomax-like distributions.

Download Full-text

Kumaraswamy Generalized Power Lomax Distributionand Its Applications

Stats ◽

10.3390/stats4010003 ◽

2021 ◽

Vol 4 (1) ◽

pp. 28-45

Author(s):

Vasili B.V. Nagarjuna ◽

R. Vishnu Vardhan ◽

Christophe Chesneau

Keyword(s):

Hazard Rate ◽

Real Data ◽

Rate Function ◽

Maximum Likelihood Estimates ◽

Parameter Estimates ◽

Parameter Distribution ◽

Data Sets ◽

Lomax Distribution ◽

Entropy Measures ◽

Modeling Behavior

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.

Download Full-text