scholarly journals Harris Extended Power Lomax Distribution: Properties, Inference and Applications

2021 ◽  
Vol 10 (4) ◽  
pp. 77
Author(s):  
Adebisi Ade Ogunde ◽  
Victoria Eshomomoh Laoye ◽  
Ogbonnaya Nzie Ezichi ◽  
Kayode Oguntuase Balogun
Keyword(s):  
Time Distribution ◽  
Lorenz Curve ◽  
Life Time ◽  
Lomax Distribution ◽  
Proposed Model ◽  
Method Of Maximum Likelihood ◽  
Distribution Parameters ◽  
Rate Functions ◽  
New Distribution ◽  
Extended Power

In this work, we present a five-parameter life time distribution called Harris power Lomax (HPL)  distribution which is obtained by convoluting the Harris-G distribution and the Power Lomax distribution. When compared to the existing distributions, the new distribution exhibits a very flexible probability functions; which may be increasing, decreasing, J, and reversed J shapes been observed for the probability density and hazard rate functions. The structural properties of the new distribution are studied in detail which includes: moments, incomplete moment, Renyl entropy, order statistics, Bonferroni curve, and Lorenz curve etc. The HPL  distribution parameters are estimated by using the method of maximum likelihood. Monte Carlo simulation was carried out to investigate the performance of MLEs. Aircraft wind shield data and Glass fibre data applications demonstrate the applicability of the proposed model.

scholarly journals Reliability Analysis of the New Exponential Inverted Topp–Leone Distribution with Applications

Entropy ◽  
2021 ◽  
Vol 23 (12) ◽  
pp. 1662
Author(s):  
Ahmed Sayed M. Metwally ◽  
Amal S. Hassan ◽  
Ehab M. Almetwally ◽  
B M Golam Kibria ◽  
Hisham M. Almongy
Keyword(s):  
Reliability Analysis ◽  
Confidence Intervals ◽  
Hazard Rate ◽  
Shape Parameter ◽  
Quantile Function ◽  
Proposed Model ◽  
Distribution Parameters ◽  
Rate Functions ◽  
New Distribution ◽  
Skewness And Kurtosis

The inverted Topp–Leone distribution is a new, appealing model for reliability analysis. In this paper, a new distribution, named new exponential inverted Topp–Leone (NEITL) is presented, which adds an extra shape parameter to the inverted Topp–Leone distribution. The graphical representations of its density, survival, and hazard rate functions are provided. The following properties are explored: quantile function, mixture representation, entropies, moments, and stress–strength reliability. We plotted the skewness and kurtosis measures of the proposed model based on the quantiles. Three different estimation procedures are suggested to estimate the distribution parameters, reliability, and hazard rate functions, along with their confidence intervals. Additionally, stress–strength reliability estimators for the NEITL model were obtained. To illustrate the findings of the paper, two real datasets on engineering and medical fields have been analyzed.

scholarly journals Transmuted Mukherjee-Islam Distribution: A Generalization of Mukherjee-Islam Distribution

2017 ◽  
Vol 9 (4) ◽  
pp. 135
Author(s):  
Loai M. A. Al-Zou'bi
Keyword(s):  
Hazard Rate ◽  
Maximum Likelihood Method ◽  
Continuous Distribution ◽  
Quantile Function ◽  
Descriptive Statistics ◽  
Likelihood Method ◽  
Distribution Parameters ◽  
Rate Functions ◽  
Mean Variance ◽  
New Distribution

A new continuous distribution is proposed in this paper. This distribution is a generalization of Mukherjee-Islam distribution using the quadratic rank transmutation map. It is called transmuted Mukherjee-Islam distribution (TMID). We have studied many properties of the new distribution: Reliability and hazard rate functions. The descriptive statistics: mean, variance, skewness, kurtosis are also studied. Maximum likelihood method is used to estimate the distribution parameters. Order statistics and Renyi and Tsallis entropies were also calculated. Furthermore, the quantile function and the median are calculated.

scholarly journals A Lomax-inverse Lindley Distribution: Model, Properties and Applications to Lifetime Data

2019 ◽  
pp. 1-28
Author(s):  
Terna Godfrey Ieren ◽  
Peter Oluwaseun Koleoso ◽  
Adana’a Felix Chama ◽  
Innocent Boyle Eraikhuemen ◽  
Nasiru Yakubu
Keyword(s):  
Likelihood Estimation ◽  
Quantile Function ◽  
Distribution Model ◽  
Lindley Distribution ◽  
Limiting Behavior ◽  
Proposed Model ◽  
Method Of Maximum Likelihood ◽  
Inverse Lindley Distribution ◽  
New Distribution ◽  
Better Than

This article proposed a new extension of the Inverse Lindley distribution called “Lomax-Inverse Lindley distribution” which is more flexible compared to the Inverse Lindley distribution and other similar models. The paper derives and discusses some Statistical properties of the new distribution which include the limiting behavior, quantile function, reliability functions and distribution of order statistics. The parameters of the new model are estimated by method of maximum likelihood estimation. Conclusively, three lifetime datasets were used to evaluate the usefulness of the proposed model and the results indicate that the proposed extension is more flexible and performs better than the other distributions considered in this study.

scholarly journals The Marshall-Olkin Extended Power Lomax Distribution with Applications

2020 ◽  
pp. 331-341
Author(s):  
JIJU GILLARIOSE ◽  
Lishamol Tomy
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Simulated Data ◽  
Likelihood Estimation ◽  
Real Data ◽  
Limiting Distributions ◽  
Lomax Distribution ◽  
New Distribution ◽  
Extended Power

In this article, we dened a new four-parameter model called Marshall-Olkin extended power Lomax distribution and studied its properties. Limiting distributions of sample maxima and sample minima are derived. The reliability of a system when both stress and strength follows the new distribution is discussed and associated characteristics are computed for simulated data. Finally, utilizing maximum likelihood estimation, the goodness of the distribution is tested for real data.

An Advanced Discrete Model with Applications in Medical Science

2018 ◽  
Vol 09 (02) ◽  
pp. 1850001
Author(s):  
Bilal Ahmad Para ◽  
Tariq Rashid Jan
Keyword(s):  
Count Data ◽  
Discrete Model ◽  
Medical Science ◽  
Real Life ◽  
Medical Sciences ◽  
Proposed Model ◽  
Specific Parameter ◽  
Rate Functions ◽  
Two Parameter ◽  
New Distribution

In this paper, we introduce a new discrete model by compounding two parameter discrete Weibull distribution with Beta distribution of first kind. The proposed model can be nested to different compound distributions on specific parameter settings. The model is a good competitive for zero-inflated models. In addition, we present the basic properties of the new distribution and discuss unimodality, failure rate functions and index of dispersion. Finally, the model is examined with real-life count data from medical sciences to investigate the suitability of the proposed model.

scholarly journals On the inferences and applications of transmuted exponential Lomax distribution

2018 ◽  
Vol 6 (1) ◽  
pp. 30
Author(s):  
Umar Kabir ◽  
Terna Godfrey IEREN
Keyword(s):  
Real Life ◽  
Likelihood Estimation ◽  
Cumulative Distribution ◽  
Data Sets ◽  
Lomax Distribution ◽  
Real Life Data ◽  
Method Of Maximum Likelihood ◽  
Probability Density Function Pdf ◽  
New Distribution ◽  
Better Than

This article proposed a new distribution referred to as the transmuted Exponential Lomax distribution as an extension of the popular Lomax distribution in the form of Exponential Lomax by using the Quadratic rank transmutation map proposed and studied in earlier research. Using the transmutation map, we defined the probability density function (PDF) and cumulative distribution function (CDF) of the transmuted Exponential Lomax distribution. Some properties of the new distribution were extensively studied after derivation. The estimation of the distribution’s parameters was also done using the method of maximum likelihood estimation. The performance of the proposed probability distribution was checked in comparison with some other generalizations of Lomax distribution using three real-life data sets. The results obtained indicated that TELD performs better than the other distributions comprising power Lomax, Exponential-Lomax, and the Lomax distributions.

scholarly journals Type II Topp Leone Power Lomax Distribution with Applications

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 4 ◽  
Author(s):  
Sanaa Al-Marzouki ◽  
Farrukh Jamal ◽  
Christophe Chesneau ◽  
Mohammed Elgarhy
Keyword(s):  
Applied Sciences ◽  
Likelihood Method ◽  
Type Ii ◽  
Lifetime Distributions ◽  
Related Model ◽  
Lomax Distribution ◽  
Mathematical Properties ◽  
Rate Functions ◽  
New Distribution ◽  
Better Than

In many areas of applied sciences, the last step of a study often consists in analyzing in depth the collected data. Among all the kinds of data, the lifetime data are well-known to convey a great deal of information whose capture is necessary to identify one or more key phenomena. In this regards, numerous mathematical models have been proposed, including those based on lifetime distributions. In this paper, we introduce a new four-parameter lifetime distribution based on the type II Topp-Leone-G family and the power Lomax distribution. In comparison to the existing distributions, the new one is characterized by very flexible probability functions: increasing, decreasing, J, and reverse J shapes are observed for the probability density and hazard rate functions, giving first signs on the potential of adaptability of the related model. With this idea in mind, the new distribution is studied in detail, from both the theoretical and applied sides. After showing its main mathematical properties, the related model is investigated with estimation of the parameters by the maximum likelihood method. We applied it to two practical datasets, including the well-know aircraft windshield data. We show that the new model performs better than several modern adversary models, motivating its use in an applied setting.

scholarly journals Exponentiated Exponential-Exponentiated Weibull Linear Mixed Distribution: Properties and Applications

2020 ◽  
pp. 517-527
Author(s):  
Salman Abbas ◽  
Muhammad Mohsin ◽  
Saman Hanif Shahbaz ◽  
Muhammad Qaiser Shahbaz
Keyword(s):  
Real Life ◽  
Moment Generating Function ◽  
Estimation Of Parameters ◽  
Data Set ◽  
Real Life Data ◽  
Proposed Model ◽  
Method Of Maximum Likelihood ◽  
Exponentiated Weibull ◽  
Rate Functions ◽  
Coefficient Of Skewness

In this article we have discussed linear mixing of two exponentiated distribution. The proposed model is named as exponentiated exponential-exponentiated Weibull (EE-EW) distribution. The proposed distribution generalize several existing distributions. We study several characteristics of the proposed distribution including moment, moment generating function, reliability and hazard rate functions. An empirical study is presented for mean, variance, coefficient of skewness, and coefficient of kurtosis. The method of maximum likelihood is used for the estimation of parameters. For the illustration purpose, we have use two real-life data set for application. The results justify the capability of the new model.

scholarly journals Marshall-Olkin Lehmann Lomax Distribution: Theory, Statistical Properties, Copulas and Real Data Modeling

2021 ◽  
pp. 509-530
Author(s):  
Mohamed Aboraya
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimators ◽  
Real Data ◽  
Unknown Parameters ◽  
Clayton Copula ◽  
Lomax Distribution ◽  
Mean Squared Errors ◽  
Method Of Maximum Likelihood ◽  
Coefficient Of Skewness ◽  
New Distribution

In this work, a new four-parameter lifetime probability distribution called the Marshall-Olkin Lehmann Lomax distribution is defined and studied. The density function of the new distribution "asymmetric right skewed" and "symmetric" and the corresponding hazard rate can be monotonically increasing, increasing-constant, constant, upside down and monotonically decreasing. The coefficient of skewness can be negative and positive. We derive some new bivariate versions via Farlie Gumbel Morgenstern family, modified Farlie Gumbel Morgenstern family, Clayton Copula and Renyi's entropy.The method of maximum likelihood is used to estimate the unknown parameters. Using "biases" and "mean squared errors", a simulation study is performed for assessing the finite behavior of the maximum likelihood estimators.

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