Mathematical properties of the Kumaraswamy-Lindley distribution and its applications

2017 ◽  
Vol 5 (1) ◽  
pp. 17
Author(s):  
Hamdy Salem ◽  
Abd-Elwahab Hagag
Keyword(s):  
Hazard Function ◽  
Likelihood Estimation ◽  
Real Data ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Least Square ◽  
Estimation Of Parameters ◽  
Least Square Estimation ◽  
Mathematical Properties ◽  
Composite Distribution

In this paper, a composite distribution of Kumaraswamy and Lindley distributions namely, Kumaraswamy-Lindley Kum-L distribution is introduced and studied. The Kum-L distribution generalizes sub-models for some widely known distributions. Some mathematical properties of the Kum-L such as hazard function, quantile function, moments, moment generating function and order statistics are obtained. Estimation of parameters for the Kum-L using maximum likelihood estimation and least square estimation techniques are provided. To illustrate the usefulness of the proposed distribution, simulation study and real data example are used.

scholarly journals Transmutation of the two parameters Rayleigh distribution

2016 ◽  
Vol 4 (2) ◽  
pp. 95
Author(s):  
Ehsan Ullah ◽  
Mirza Shahzad
Keyword(s):  
Real Data ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Rayleigh Distribution ◽  
Least Square ◽  
Least Square Estimation ◽  
Proposed Model ◽  
Method Of Least Square ◽  
Two Parameters ◽  
Mean Variance

In this study, transmuted two parameters Rayleigh distribution is proposed using quadratic rank transmutation map. This proposed distribution is more flexible and versatile than two parameters Rayleigh distribution. Some properties of the proposed distribution are derived such as moments, moment generating function, mean, variance, median, quantile function, reliability, and hazard function. The parameter estimation is approached through the method of least square estimation. The th and joint order statistics are also derived for the proposed distribution. The application of proposed model illustrated and compared using real data.

scholarly journals The Half-Logistic Generalized Weibull Distribution

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Masood Anwar ◽  
Amna Bibi
Keyword(s):  
Weibull Distribution ◽  
Information Matrix ◽  
Likelihood Estimation ◽  
Real Data ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Type I ◽  
Failure Rate Function ◽  
New Model ◽  
Compound Distribution

A new three-parameter generalized distribution, namely, half-logistic generalized Weibull (HLGW) distribution, is proposed. The proposed distribution exhibits increasing, decreasing, bathtub-shaped, unimodal, and decreasing-increasing-decreasing hazard rates. The distribution is a compound distribution of type I half-logistic-G and Dimitrakopoulou distribution. The new model includes half-logistic Weibull distribution, half-logistic exponential distribution, and half-logistic Nadarajah-Haghighi distribution as submodels. Some distributional properties of the new model are investigated which include the density function shapes and the failure rate function, raw moments, moment generating function, order statistics, L-moments, and quantile function. The parameters involved in the model are estimated using the method of maximum likelihood estimation. The asymptotic distribution of the estimators is also investigated via Fisher’s information matrix. The likelihood ratio (LR) test is used to compare the HLGW distribution with its submodels. Some applications of the proposed distribution using real data sets are included to examine the usefulness of the distribution.

scholarly journals The Marshall–Olkin Generalized Inverse Weibull Distribution: Properties and Application

2019 ◽  
Vol 13 (2) ◽  
pp. 54
Author(s):  
Hamdy M. Salem
Keyword(s):  
Weibull Distribution ◽  
Hazard Function ◽  
Information Matrix ◽  
Real Data ◽  
Moment Generating Function ◽  
Least Square ◽  
Superior Performance ◽  
Inverse Weibull Distribution ◽  
Interval Estimators ◽  
New Distribution

In this paper, a new distribution namely, The Marshall–OlkinGeneralized Inverse Weibull Distribution is illustrated and studied. The new distribution is very flexible and contains sub-models such asinverse exponential, inverse Rayleigh, Weibull, inverse Weibull, Marshall–Olkininverse Weibull and Fréchetdistributions. Also, the hazard function of the new distribution can produce variety of forms:an increase, a decrease and an upside-down bathtub. Some properties such as hazard function, quintile function, entropy, moment generating function and order statistics are obtained. Different estimation approaches namely, maximum likelihood estimators, interval estimators, least square estimators, fisher information matrix and asymptotic confidence intervals are described. To illustrate the superior performance of the proposed distribution, a simulation study and a real data analysis are investigated against other models.

scholarly journals A New Probability Distribution Family Arising from Truncated Power Lomax Distribution with Application to Weibull Model

2020 ◽  
pp. 661-674
Author(s):  
Amal Hassan ◽  
Mohamed Sabry ◽  
Ahmed Elsehetry
Keyword(s):  
Likelihood Estimation ◽  
Real Data ◽  
Quantile Function ◽  
Weibull Model ◽  
Moment Generating Function ◽  
Distribution Model ◽  
Mean Deviation ◽  
Data Set ◽  
Lifetime Distributions ◽  
Lomax Distribution

The truncated distributions have been widely studied, mainly in life-testing and reliability analysis.  In this paper, we introduce a new right truncated generator related to power Lomax distribution, referred to right truncated power Lomax--G family. The proposed family is a generalization of recently [0, 1] truncated Lomax-G family. Statistical properties like; moments, moment generating function, probability weighted moments, quantile function, mean deviation, order statistics and Rényi entropy are derived. Five new sub-models from the truncated family are presented. Maximum likelihood estimation is investigated and simulation issues are discussed for truncated power Lomax Weibull model as particular case from the family. The flexibility of the truncated power Lomax Weibull is assessed by applying it to a real data set. The application indicates that the truncated power Lomax Weibull distribution model can give better fits than other well-known lifetime distributions.

scholarly journals Exponentiated Cubic Transmuted Weibull Distribution: Properties and Application

2021 ◽  
pp. 1-11
Author(s):  
Oseghale O. I. ◽  
Akomolafe A. A. ◽  
Gayawan E.
Keyword(s):  
Weibull Distribution ◽  
Real Life ◽  
Likelihood Estimation ◽  
Real Data ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Data Sets ◽  
Estimation Technique ◽  
Life Data ◽  
Real Life Data

This work is focused on the four parameters Exponentiated Cubic Transmuted Weibull distribution which mostly found its application in reliability analysis most especially for data that are non-monotone and Bi-modal. Structural properties such as moment, moment generating function, Quantile function, Renyi entropy, and order statistics were investigated. The maximum likelihood estimation technique was used to estimate the parameters of the distribution. Application to two real-life data sets shows the applicability of the distribution in modeling real data.

scholarly journals The Zubair-dagum Distribution

2021 ◽  
pp. 25-35
Author(s):  
O. R. Uwaeme ◽  
N. P. Akpan
Keyword(s):  
Real Life ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Parameter Estimates ◽  
Mathematical Properties ◽  
Dagum Distribution ◽  
Maximum Likelihood Estimation Method ◽  
New Distribution

This article examines the flexibility of the Zubair-G family of distribution using the Dagum distribution. The proposed distribution is called the Zubair-Dagum distribution. The various mathematical properties of this distribution such as the Quantile function, Moments, Moment generating function, Reliability analysis, Entropy and Order statistics were obtained. The parameter estimates of the proposed distribution were also derived and estimated using the maximum likelihood estimation method. The new distribution is right skewed and has various bathtub and monotonically decreasing shapes. Our numerical illustrations using two real-life datasets substantiate the applicability, flexibility and superiority of the proposed distribution over competing distributions.

scholarly journals A New Odd Lindley-Gompertz Distribution: Its Properties and Applications

2020 ◽  
pp. 29-47
Author(s):  
Omolola Dorcas Atanda ◽  
Tajan Mashingil Mabur ◽  
Gerald Ikechukwu Onwuka
Keyword(s):  
Generating Function ◽  
Hazard Function ◽  
Goodness Of Fit ◽  
Real Life ◽  
Likelihood Estimation ◽  
Quantile Function ◽  
Reliability Function ◽  
Moment Generating Function ◽  
Gompertz Distribution ◽  
Better Than

This article presents a comprehensive study of an odd Lindley-Gompertz distribution which has already been proposed in the literature but without any properties. The present study unlike the previous one has considered the derivation of several properties of the odd Lindley-Gompertz distribution with their graphical representations and discussions which has not been done in the first proposition of the distribution.  The study looks at properties such as survival (or reliability) function, the hazard function, the cumulative hazard function, the reverse hazard function, the odds function, quantile function, moments, moment generating function, characteristic function, cumulant generating function, distribution of order statistics and maximum likelihood estimation of the distribution’s parameters none of which was treated by the previous author of the model. An illustration to evaluate the goodness-of-fit of the odd Lindley-Gompertz distribution has also been done using two real life datasets and the results show that the model fits the datasets better than the five other distributions considered in this present study.

scholarly journals Lomax-Gumbel {Fréchet}: A New Distribution

2019 ◽  
pp. 1-19
Author(s):  
M. R. Mahmoud ◽  
R. M. Mandouh ◽  
R. E. Abdelatty
Keyword(s):  
Generating Function ◽  
Simulation Study ◽  
Hazard Function ◽  
Real Data ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Data Sets ◽  
Function Estimate ◽  
Frechet Distribution ◽  
New Distribution

In this paper the T-R{Y} framework is used for proposing a new distribution that called The Lomax-Gumbel{Frechet} distribution. We study in details the properties of this distribution including hazard function, quantile Function, the skewness, the kurtosis, transformation, Renyi entropy, and moment generating function. Estimate of the parameters will be obtained using the MLE method. We present a simulation study and t the distribution to two real data sets.

scholarly journals Kumaraswamy Distribution Based on Alpha Power Transformation Methods

2021 ◽  
pp. 14-29
Author(s):  
H. E. Hozaien ◽  
G. R. AL Dayian ◽  
A. A. EL-Helbawy
Keyword(s):  
Residual Life ◽  
Likelihood Estimation ◽  
Real Data ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Mean Residual Life ◽  
Alpha Power ◽  
Unknown Parameters ◽  
Data Set ◽  
Kumaraswamy Distribution

In this paper, the alpha power Kumaraswamy distribution, new alpha power transformed Kumaraswamy distribution and new extended alpha power transformed Kumaraswamy distribution are presented. Some statistical properties of the three distributions are derived including quantile function, moments and moment generating function, mean residual life and order statistics. Estimation of the unknown parameters based on maximum likelihood estimation are obtained. A simulation study is carried out. Finally, a real data set is applied.

An alternative distribution to Lindley and Power Lindley distributions with characterizations, different estimation methods and data applications

2020 ◽  
Vol 70 (4) ◽  
pp. 953-978
Author(s):  
Mustafa Ç. Korkmaz ◽  
G. G. Hamedani
Keyword(s):  
Hazard Function ◽  
Mixture Distribution ◽  
Real Data ◽  
Quantile Function ◽  
Estimation Methods ◽  
Data Sets ◽  
Unknown Parameters ◽  
Lorenz Curves ◽  
Proposed Model ◽  
New Distribution

AbstractThis paper proposes a new extended Lindley distribution, which has a more flexible density and hazard rate shapes than the Lindley and Power Lindley distributions, based on the mixture distribution structure in order to model with new distribution characteristics real data phenomena. Its some distributional properties such as the shapes, moments, quantile function, Bonferonni and Lorenz curves, mean deviations and order statistics have been obtained. Characterizations based on two truncated moments, conditional expectation as well as in terms of the hazard function are presented. Different estimation procedures have been employed to estimate the unknown parameters and their performances are compared via Monte Carlo simulations. The flexibility and importance of the proposed model are illustrated by two real data sets.

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