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.

scholarly journals The Three-parameters Marshall-Olkin Generalized Weibull Model with Properties and Different Applications to Real Data Sets

2020 ◽  
pp. 675-688
Author(s):  
Mohamed G. Khalil ◽  
Wagdy M. Kamel
Keyword(s):  
Maximum Likelihood ◽  
Likelihood Estimation ◽  
Real Data ◽  
Weibull Model ◽  
Parametric Model ◽  
Data Sets ◽  
Unknown Parameters ◽  
Graphical Simulation ◽  
Method Of Maximum Likelihood ◽  
New Distribution

A new three-parameter life parametric model called the Marshall-Olkin generalized Weibull is defined and studied. Relevant properties are mathematically derived and analyzed. The new density exhibits various important symmetric and asymmetric shapes with different useful kurtosis. The new failure rate can be “constant”, “upside down-constant (reversed U-HRF-constant)”, “increasing then constant”, “monotonically increasing”, “J-HRF” and “monotonically decreasing”. The method of maximum likelihood is employed to estimate the unknown parameters. A graphical simulation is performed to assess the performance of the maximum likelihood estimation. We checked and proved empirically the importance, applicability and flexibility of the new Weibull model in modeling various symmetric and asymmetric types of data. The new distribution has a high ability to model different symmetric and asymmetric types of data.

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.

scholarly journals The Gumbel- Pareto Distribution: Theory and Applications

2019 ◽  
Vol 16 (4) ◽  
pp. 0937
Author(s):  
Saad Et al.
Keyword(s):  
Maximum Likelihood ◽  
Pareto Distribution ◽  
Real Data ◽  
Model Parameters ◽  
Numerical Illustration ◽  
Data Set ◽  
Mathematical Properties ◽  
Method Of Maximum Likelihood ◽  
First Time ◽  
New Distribution

In this paper, for the first time we introduce a new four-parameter model called the Gumbel- Pareto distribution by using the T-X method. We obtain some of its mathematical properties. Some structural properties of the new distribution are studied. The method of maximum likelihood is used for estimating the model parameters. Numerical illustration and an application to a real data set are given to show the flexibility and potentiality of the new model.

scholarly journals SOME PROPERTIES OF BETA TRANSMUTED DAGUM DISTRIBUTION WITH APPLICATIONS

2020 ◽  
Vol 4 (2) ◽  
pp. 327-340
Author(s):  
Ahmed Ali Hurairah ◽  
Saeed A. Hassen
Keyword(s):  
Maximum Likelihood ◽  
Likelihood Estimation ◽  
Real Data ◽  
Moment Generating Function ◽  
Model Parameters ◽  
Data Set ◽  
New Family ◽  
Method Of Maximum Likelihood ◽  
Dagum Distribution ◽  
New Distribution

In this paper, we introduce a new family of continuous distributions called the beta transmuted Dagum distribution which extends the beta and transmuted familys. The genesis of the beta distribution and transmuted map is used to develop the so-called beta transmuted Dagum (BTD) distribution. The hazard function, moments, moment generating function, quantiles and stress-strength of the beta transmuted Dagum distribution (BTD) are provided and discussed in detail. The method of maximum likelihood estimation is used for estimating the model parameters. A simulation study is carried out to show the performance of the maximum likelihood estimate of parameters of the new distribution. The usefulness of the new model is illustrated through an application to a real data set.

scholarly journals Discriminating between the normal inverse Gaussian and generalized hyperbolic skew-t distributions with a follow-up the stock exchange data

2018 ◽  
Vol 28 (2) ◽  
pp. 185-199
Author(s):  
Hanieh Panahi
Keyword(s):  
Maximum Likelihood ◽  
Goodness Of Fit ◽  
Stock Exchange ◽  
Maximum Likelihood Estimators ◽  
Real Data ◽  
Information Criteria ◽  
Inverse Gaussian ◽  
Unknown Parameters ◽  
Normal Inverse Gaussian ◽  
Exchange Data

The statistical methods for the financial returns play a key role in measuring the goodness-of-fit of a given distribution to real data. As is well known, the normal inverse Gaussian (NIG) and generalized hyperbolic skew-t (GHST) distributions have been found to successfully describe the data of the returns from financial market. In this paper, we mainly consider the discrimination between these distributions. It is observed that the maximum likelihood estimators (MLEs) cannot be obtained in closed form. We propose to use the EM algorithm to compute the maximum likelihood estimators. The approximate confidence intervals of the unknown parameters have been constructed. We then perform a number of goodness-of-fit tests to compare the NIG and GHST distributions for the stock exchange data. Moreover, the Vuong type test, based on the Kullback-Leibler information criteria, has been considered to select the most appropriate candidate model. An important implication of the present study is that the GHST distribution function, in contrast to NIG distribution, may describe more appropriate for the proposed data.

scholarly journals A Study on Properties and Applications of a Lomax Gompertz-Makeham Distribution

2019 ◽  
pp. 1-27
Author(s):  
Innocent Boyle Eraikhuemen ◽  
Terna Godfrey Ieren ◽  
Tajan Mashingil Mabur ◽  
Mohammed Sa’ad ◽  
Samson Kuje ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Probability Distributions ◽  
Real Life ◽  
Likelihood Estimation ◽  
The Other ◽  
Unknown Parameters ◽  
Method Of Maximum Likelihood ◽  
Compound Model ◽  
New Distribution

The article presents an extension of the Gompertz-Makeham distribution using the Lomax generator of probability distributions. This generalization of the Gompertz-Makeham distribution provides a more skewed and flexible compound model called Lomax Gompertz-Makeham distribution. The paper derives and discusses some Mathematical and Statistical properties of the new distribution. The unknown parameters of the new model are estimated via the method of maximum likelihood estimation. In conclusion, the new distribution is applied to two real life datasets together with two other related models to check its flexibility or performance and the results indicate that the proposed extension is more flexible compared to the other two distributions considered in the paper based on the two datasets used.

scholarly journals The Log-logistic Weibull Distribution with Applications to Lifetime Data

2016 ◽  
Vol 45 (3) ◽  
pp. 43-69 ◽  
Author(s):  
Broderick Oluyede ◽  
Susan Foya ◽  
Gayan Warahena-Liyanage ◽  
Shujiao Huang
Keyword(s):  
Maximum Likelihood ◽  
Real Data ◽  
Quantile Function ◽  
Lorenz Curves ◽  
Conditional Moments ◽  
Method Of Maximum Likelihood ◽  
L Moments ◽  
New Distribution ◽  
Generalized Distribution ◽  
Func Tion

In this paper, a new generalized distribution called the log-logisticWeibull (LLoGW) distribution is developed and presented. This dis-tribution contain the log-logistic Rayleigh (LLoGR), log-logistic expo-nential (LLoGE) and log-logistic (LLoG) distributions as special cases.The structural properties of the distribution including the hazard func-tion, reverse hazard function, quantile function, probability weightedmoments, moments, conditional moments, mean deviations, Bonferroniand Lorenz curves, distribution of order statistics, L-moments and Renyientropy are derived. Method of maximum likelihood is used to estimatethe parameters of this new distribution. A simulation study to examinethe bias, mean square error of the maximum likelihood estimators andwidth of the condence intervals for each parameter is presented. Finally, real data examples are presented to illustrate the usefulness and applicability of the model.

scholarly journals The Generalized Odd Generalized Exponential Fréchet Model: Univariate, Bivariate and Multivariate Extensions with Properties and Applications to the Univariate Version

2020 ◽  
pp. 529-544 ◽  
Author(s):  
Hisham Abdel Hamid Elsayed ◽  
Haitham M. Yousof
Keyword(s):  
Maximum Likelihood ◽  
Generating Functions ◽  
Residual Life ◽  
Maximum Likelihood Estimators ◽  
Real Data ◽  
Simple Type ◽  
Data Sets ◽  
New Model ◽  
Clayton Copula ◽  
Stochastic Properties

A new univariate extension of the Fréchet distribution is proposed and studied. Some of its fundamental statistical properties such as stochastic properties, ordinary and incomplete moments, moments generating functions, residual life and reversed residual life functions, order statistics, quantile spread ordering, Rényi, Shannon and q-entropies are derived. A simple type Copula based construction using Morgenstern family and via Clayton Copula is employed to derive many bivariate and multivariate extensions of the new model. We assessed the performance of the maximum likelihood estimators using a simulation study. The importance of the new model is shown by means of two applications to real data sets.

scholarly journals A New Lindley-Burr XII Distribution: Model, Properties and Applications

2021 ◽  
Vol 10 (4) ◽  
pp. 33
Author(s):  
Boikanyo Makubate ◽  
Broderick Oluyede ◽  
Morongwa Gabanakgosi
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimators ◽  
Likelihood Estimation ◽  
Real Data ◽  
Distribution Model ◽  
Model Parameters ◽  
Data Sets ◽  
Mean Square ◽  
Conditional Moments ◽  
New Distribution

A new distribution called the Lindley-Burr XII (LBXII) distribution is proposed and studied. Some structural properties of the new distribution including moments, conditional moments, distribution of the order statistics and R´enyi entropy are derived. Maximum likelihood estimation technique is used to estimate the model parameters. A simulation study to examine the bias and mean square error of the maximum likelihood estimators is presented and applications to real data sets in order to illustrate the usefulness of the new distribution are given.

The exponentiated exponential burr XII distribution: Theory and application to lifetime data

2020 ◽  
pp. 1-14
Author(s):  
Majdah M. Badr
Keyword(s):  
Maximum Likelihood ◽  
Goodness Of Fit ◽  
Maximum Likelihood Estimators ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Significant Heterogeneity ◽  
Lifetime Data ◽  
Fit Statistics ◽  
Mathematical Properties ◽  
New Distribution

Lifetime data collected from reliability tests are among data that often exhibit significant heterogeneity caused by variations in manufacturing which make standard lifetime models inadequate. In this paper we introduce a new lifetime distribution derived from T-X family technique called exponentiated exponential Burr XII (EE-BXII) distribution. We establish various mathematical properties. The maximum likelihood estimates (MLE) for the EE-BXII parameters are derived. We estimate the precision of the maximum likelihood estimators via simulation study. Some numerical illustrations are performed to study the behavior of the obtained estimators. Finally the model is applied to a real dataset. We apply goodness of fit statistics and graphical tools to examine the adequacy of the EE-BXII distribution. The importance of this research lies in deriving a new distribution under the name EE-BXII, which is considered the best distributions in analyzing data of life times at present if compared to many distributions in analysis real data.

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