scholarly journals The Transmuted Marshall-Olkin Fr\'{e}chet Distribution: Properties and Applications

2015 ◽  
Vol 4 (4) ◽  
pp. 132 ◽  
Author(s):  
Ahmed Z. Afify ◽  
G. G. Hamedani ◽  
Indranil Ghosh ◽  
M. E. Mead
Keyword(s):  
Maximum Likelihood ◽  
Order Statistics ◽  
Maximum Likelihood Method ◽  
Real Life ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Sets ◽  
Life Data ◽  
Real Life Data ◽  
Lifetime Model

<p>This paper introduces a new four-parameter lifetime model, which extends the Marshall-Olkin Fr\'{e}chet distribution introduced by Krishna et al. (2013), called the transmuted Marshall-Olkin Fr\'{e}chet distribution. Various structural properties including ordinary and incomplete moments, quantile and generating function, R\'{e}nyi and q-entropies and order statistics are<br />derived. The maximum likelihood method is used to estimate the model parameters. We illustrate the superiority of the proposed distribution over other existing distributions in the literature in modeling two real life data sets.</p>

scholarly journals A New Kumaraswamy Generalized Family of Distributions with Properties, Applications, and Bivariate Extension

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1989
Author(s):  
Muhammad H. Tahir ◽  
Muhammad Adnan Hussain ◽  
Gauss M. Cordeiro ◽  
M. El-Morshedy ◽  
M. S. Eliwa
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Real Life ◽  
Unit Interval ◽  
Likelihood Method ◽  
Data Sets ◽  
Data Set ◽  
Life Data ◽  
Real Life Data ◽  
Family Of Distributions

For bounded unit interval, we propose a new Kumaraswamy generalized (G) family of distributions through a new generator which could be an alternate to the Kumaraswamy-G family proposed earlier by Cordeiro and de Castro in 2011. This new generator can also be used to develop alternate G-classes such as beta-G, McDonald-G, Topp-Leone-G, Marshall-Olkin-G, and Transmuted-G for bounded unit interval. Some mathematical properties of this new family are obtained and maximum likelihood method is used for the estimation of G-family parameters. We investigate the properties of one special model called the new Kumaraswamy-Weibull (NKwW) distribution. Parameters of NKwW model are estimated by using maximum likelihood method, and the performance of these estimators are assessed through simulation study. Two real life data sets are analyzed to illustrate the importance and flexibility of the proposed model. In fact, this model outperforms some generalized Weibull models such as the Kumaraswamy-Weibull, McDonald-Weibull, beta-Weibull, exponentiated-generalized Weibull, gamma-Weibull, odd log-logistic-Weibull, Marshall-Olkin-Weibull, transmuted-Weibull and exponentiated-Weibull distributions when applied to these data sets. The bivariate extension of the family is also proposed, and the estimation of parameters is dealt. The usefulness of the bivariate NKwW model is illustrated empirically by means of a real-life data set.

scholarly journals A New Kumaraswamy Generalized Family of Distributions with Properties, Applications and Bivariate Extension

2020 ◽  
Author(s):  
Muhammad H. Tahir ◽  
Muhammad Adnan Hussain ◽  
Gauss Cordeiro ◽  
Mahmoud El-Morshedy ◽  
Mohammed S. Eliwa
Keyword(s):  
Maximum Likelihood ◽  
Real Life ◽  
Unit Interval ◽  
Likelihood Method ◽  
Data Sets ◽  
Data Set ◽  
Life Data ◽  
Real Life Data ◽  
The Family ◽  
Family Of Distributions

For bounded unit interval, we propose a new Kumaraswamy generalized (G) family of distributions from a new generator which could be an alternate to the Kumaraswamy-G family proposed earlier by Cordeiro and de-Castro in 2011. This new generator can also be used to develop alternate G-classes such as beta-G, McDonald-G, Topp-Leone-G, Marshall-Olkin-G and Transmuted-G for bounded unit interval. Some mathematical properties of this new family are obtained and maximum likelihood method is used for estimating the family parameters. We investigate the properties of one special model called a new Kumaraswamy-Weibull (NKwW) distribution. Parameter estimation is dealt and maximum likelihood estimators are assessed through simulation study. Two real life data sets are analyzed to illustrate the importance and flexibility of this distribution. In fact, this model outperforms some generalized Weibull models such as the Kumaraswamy-Weibull, McDonald-Weibull, beta-Weibull, exponentiated-generalized Weibull, gamma-Weibull, odd log-logistic-Weibull, Marshall-Olkin-Weibull, transmuted-Weibull, exponentiated-Weibull and Weibull distributions when applied to these data sets. The bivariate extension of the family is proposed and the estimation of parameters is given. The usefulness of the bivariate NKwW model is illustrated empirically by means of a real-life data set.

scholarly journals The Discrete Type-II Half-Logistic Exponential Distribution with Applications to COVID-19 Data

2021 ◽  
pp. 921-932
Author(s):  
Muhammad Ahsan ul Haq ◽  
Ayesha Babar ◽  
Sharqa Hashmi ◽  
Abdulaziz S. Alghamdi ◽  
Ahmed Z. Afify
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Real Life ◽  
Discrete Models ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Sets ◽  
Type Ii ◽  
Two Parameter ◽  
Discrete Type

We propose a new two-parameter discrete model, called discrete Type-II half-logistics exponential (DTIIHLE) distribution using the survival discretization approach. The DTIIHLE distribution can be utilized to model COVID-19 data. The model parameters are estimated using the maximum likelihood method. A simulation study is conducted to evaluate the performance of the maximum likelihood estimators. The usefulness of the proposed distribution is evaluated using two real-life COVID-19 data sets. The DTIIHLE distribution provides a superior fit to COVID-19 data as compared with competitive discrete models including the discrete-Pareto, discrete Burr-XII, discrete log-logistic, discrete-Lindley, discrete-Rayleigh, discrete inverse-Rayleigh, and natural discrete-Lindley.

scholarly journals A New Flexible Three-Parameter Model: Properties, Clayton Copula, and Modeling Real Data

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 440 ◽  
Author(s):  
Abdulhakim A. Al-babtain ◽  
I. Elbatal ◽  
Haitham M. Yousof
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Real Data ◽  
Likelihood Method ◽  
Model Parameters ◽  
Simple Type ◽  
Data Sets ◽  
New Model ◽  
Clayton Copula ◽  
Mathematical Properties

In this article, we introduced a new extension of the binomial-exponential 2 distribution. We discussed some of its structural mathematical properties. A simple type Copula-based construction is also presented to construct the bivariate- and multivariate-type distributions. We estimated the model parameters via the maximum likelihood method. Finally, we illustrated the importance of the new model by the study of two real data applications to show the flexibility and potentiality of the new model in modeling skewed and symmetric data sets.

scholarly journals A New Family of Continuous Probability Distributions

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 194
Author(s):  
M. El-Morshedy ◽  
Fahad Sameer Alshammari ◽  
Yasser S. Hamed ◽  
Mohammed S. Eliwa ◽  
Haitham M. Yousof
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Probability Distributions ◽  
Real Life ◽  
Likelihood Method ◽  
Model Parameters ◽  
Finite Sample ◽  
Graphical Simulation ◽  
New Family ◽  
The One

In this paper, a new parametric compound G family of continuous probability distributions called the Poisson generalized exponential G (PGEG) family is derived and studied. Relevant mathematical properties are derived. Some new bivariate G families using the theorems of “Farlie-Gumbel-Morgenstern copula”, “the modified Farlie-Gumbel-Morgenstern copula”, “the Clayton copula”, and “the Renyi’s entropy copula” are presented. Many special members are derived, and a special attention is devoted to the exponential and the one parameter Pareto type II model. The maximum likelihood method is used to estimate the model parameters. A graphical simulation is performed to assess the finite sample behavior of the estimators of the maximum likelihood method. Two real-life data applications are proposed to illustrate the importance of the new family.

scholarly journals On modified Kies distribution and its applications

2017 ◽  
Vol 51 (1) ◽  
pp. 41-60
Author(s):  
C. SATHEESH KUMAR ◽  
S. H. S. DHARMAJA
Keyword(s):  
Maximum Likelihood ◽  
Hazard Function ◽  
Real Life ◽  
Simulated Data ◽  
Maximum Likelihood Estimators ◽  
Data Sets ◽  
Life Data ◽  
Real Life Data ◽  
Method Of Maximum Likelihood ◽  
Simulated Data Sets

In this paper, we consider a class of bathtub-shaped hazard function distribution through modifying the Kies distribution and investigate some of its important properties by deriving expressions for its percentile function, raw moments, stress-strength reliability measure etc. The parameters of the distribution are estimated by the method of maximum likelihood and discussed some of its reliability applications with the help of certain real life data sets. In addition, the asymptotic behavior of the maximum likelihood estimators of the parameters of the distribution is examined by using simulated data sets.

scholarly journals A Comparative Study for Weighted Rayleigh Distribution

2021 ◽  
Author(s):  
Sofi Mudasir Ahad ◽  
Sheikh Parvaiz Ahmad ◽  
Sheikh Aasimeh Rehman
Keyword(s):  
Maximum Likelihood Method ◽  
Mean Squared Error ◽  
Real Life ◽  
Rayleigh Distribution ◽  
Likelihood Method ◽  
Data Sets ◽  
Posterior Distributions ◽  
Bayes Estimators ◽  
Squared Error ◽  
Real Life Data

In this paper, Bayesian and non-Bayesian methods are used for parameter estimation of weighted Rayleigh (WR) distribution. Posterior distributions are derived under the assumption of informative and non-informative priors. The Bayes estimators and associated risks are obtained under different symmetric and asymmetric loss functions. Results are compared on the basis of posterior risk and mean square error using simulated and real life data sets. The study depicts that in order to estimate the scale parameter of the weighted Rayleigh distribution use of entropy loss function under Gumbel type II prior can be preferred. Also, Bayesian method of estimation having least values of mean squared error gives better results as compared to maximum likelihood method of estimation.

scholarly journals New Extension of Weibull Distribution: Copula, Mathematical Properties and Data Modeling

2020 ◽  
Vol 8 (4) ◽  
pp. 972-993
Author(s):  
Hanaa Elgohari ◽  
Haitham Yousof
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Likelihood Estimation ◽  
Likelihood Method ◽  
Model Parameters ◽  
Graphical Simulation ◽  
Mathematical Properties ◽  
Exponentiated Weibull ◽  
Lifetime Model ◽  
Simulation Results

This paper introduces a new flexible four-parameter lifetime model. Various of its structural properties are derived. The new density is expressed as a linear mixture of well-known exponentiated Weibull density. The maximum likelihood method is used to estimate the model parameters. Graphical simulation results to assess the performance of the maximum likelihood estimation are performed. We proved empirically the importance and flexibility of the new model in modeling four various types of data.

scholarly journals Modified generalized marshall-olkin family of distributions

2019 ◽  
Vol 7 (1) ◽  
pp. 18
Author(s):  
Muhammad Aslam ◽  
Zawar Hussain ◽  
Zahid Asghar
Keyword(s):  
Maximum Likelihood ◽  
Goodness Of Fit ◽  
Maximum Likelihood Method ◽  
Likelihood Estimation ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Sets ◽  
Goodness Of Fit Tests ◽  
New Family ◽  
Family Of Distributions

In this article, we propose a new family of distributions using the T-X family named as modified generalized Marshall-Olkin family of distributions. Comprehensive mathematical and statistical properties of this family of distributions are provided. The model parameters are estimated by maximum likelihood method. The maximum likelihood estimation under Type-II censoring is also discussed. Two lifetime data sets are used to show the suitability and applicability of the new family of distributions. For comparison purposes, different goodness of fit tests are used.  

scholarly journals On a modified Burr XII distribution having flexible hazard rate shapes

2020 ◽  
Vol 70 (1) ◽  
pp. 193-212
Author(s):  
Farrukh Jamal ◽  
Christophe Chesneau ◽  
M. Arslan Nasir ◽  
Abdus Saboor ◽  
Emrah Altun ◽  
...  
Keyword(s):  
Hazard Rate ◽  
Real Life ◽  
Stochastic Ordering ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Data Sets ◽  
Monte Carlo Simulation Study ◽  
Burr Xii Distribution ◽  
Life Data ◽  
Real Life Data

AbstractIn this paper, we propose a new three-parameter modified Burr XII distribution based on the standard Burr XII distribution and the composition technique developed by [14]. Among others, we show that this technique has the ability to significantly increase the flexibility of the former Burr XII distribution, with respect to the density and hazard rate shapes. Also, complementary theoretical aspects are studied as shapes, asymptotes, quantiles, useful expansion, moments, skewness, kurtosis, incomplete moments, moments generating function, stochastic ordering, reliability parameter and order statistics. Then, a Monte Carlo simulation study is carried out to assess the performance of the maximum likelihood estimates of the modified Burr XII model parameters. Finally, three applications to real-life data sets are presented, with models comparisons. The results are favorable for the new modified Burr XII model.

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