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 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 Extended Odd Fréchet-G Family of Distributions

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Suleman Nasiru
Keyword(s):  
Maximum Likelihood Method ◽  
Real Data ◽  
Likelihood Method ◽  
Data Sets ◽  
Data Set ◽  
New Class ◽  
New Family ◽  
Rate Functions ◽  
The Given ◽  
Family Of Distributions

The need to develop generalizations of existing statistical distributions to make them more flexible in modeling real data sets is vital in parametric statistical modeling and inference. Thus, this study develops a new class of distributions called the extended odd Fréchet family of distributions for modifying existing standard distributions. Two special models named the extended odd Fréchet Nadarajah-Haghighi and extended odd Fréchet Weibull distributions are proposed using the developed family. The densities and the hazard rate functions of the two special distributions exhibit different kinds of monotonic and nonmonotonic shapes. The maximum likelihood method is used to develop estimators for the parameters of the new class of distributions. The application of the special distributions is illustrated by means of a real data set. The results revealed that the special distributions developed from the new family can provide reasonable parametric fit to the given data set compared to other existing distributions.

scholarly journals Inverse Lomax-Exponentiated G (IL-EG) Family of Distributions: Properties and Applications

2020 ◽  
pp. 48-64
Author(s):  
Jamilu Yunusa Falgore ◽  
Sani Ibrahim Doguwa
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Moment Generating Function ◽  
Maximum Likelihood Estimates ◽  
Likelihood Method ◽  
Data Sets ◽  
Baseline Model ◽  
New Family ◽  
Family Of Distributions ◽  
Better Than

A new generator of continuous distributions called the Inverse Lomax-Exponentiated G family, which has three extra positive parameters is proposed. The structural properties of the new family that holds for any continuous baseline model including explicit density function expressions, moments, inequality measurements, moment generating function, reliability functions, Renyi and Shanon entropies, and distribution of order statistics are derived. A Monte Carlo simulation to test the efficiency of the maximum likelihood estimates is conducted. The application of the new sub-model to the two data sets using the maximum likelihood method indicates that the new model is better than the existing competitors.

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 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 Asymptotic curved normal distribution

2019 ◽  
Vol 52 (2) ◽  
pp. 173-186
Author(s):  
C. SATHEESH KUMAR ◽  
G. V. ANILA
Keyword(s):  
Maximum Likelihood ◽  
Normal Distribution ◽  
Simulation Study ◽  
Real Life ◽  
Skew Normal Distribution ◽  
Data Set ◽  
New Class ◽  
Life Data ◽  
Real Life Data ◽  
Method Of Maximum Likelihood

Here we introduce a new class of skew normal distribution as a generalization of the extended skew curved normal distribution of Kumar and Anusree (J. Statist. Res., 2017) and investigate some of its important statistical properties. The location-scale extension of the proposed class of distribution is also defined and discussed the estimation of its parameters by method of maximum likelihood. Further, a real life data set is considered for illustrating the usefulness of the model and a brief simulation study is attempted for assessing the performance of the estimators.

A likelihood approach for evaluating estimates of phylogenetic relationships among fossil taxa

Paleobiology ◽  
1998 ◽  
Vol 24 (4) ◽  
pp. 430-449 ◽  
Author(s):  
Peter J. Wagner
Keyword(s):  
Maximum Likelihood ◽  
Phylogenetic Relationships ◽  
Fossil Record ◽  
Maximum Likelihood Method ◽  
Character Evolution ◽  
Likelihood Method ◽  
Data Sets ◽  
Data Set ◽  
Parsimony Tree ◽  
Tree Length

Estimates of phylogenetic relationships among fossil taxa implicitly provide hypotheses about the quality of the fossil record. Phylogenetic inferences also provide hypotheses about character evolution. The likelihood of any hypothesis that makes predictions about two data sets is simply the likelihood of the hypothesis given the first data set times the likelihood of the same hypothesis given the second data set. In this case, data set 1 represents stratigraphy and data set 2 represents morphology. Statistical methods exist for determining the likelihood of hypothesized levels of sampling. The likelihood of a hypothesized amount of character change yielding a particular most-parsimonious solution (i.e, L[hypothesized length | parsimony length] can be evaluated with simulations. A reanalysis of hyaenid phylogeny based on published character and stratigraphic data is presented here, using the maximum likelihood method. Two trees are found, depending on assumptions about ambiguous species, which are 11 and 10 steps longer than the most parsimonious tree (61 or 60 vs. 50 steps). However, the trees invoke far less stratigraphic debt (9 or 12 units vs. 47 units as measured in Mammal Zones). An important feature of the results is that the most likely tree length given hyaenid character data is estimated to be 56 to 62 steps (depending on the model of character evolution) rather than 50 steps. The likelihood tree suggests stronger trends toward bone-crushing specializations than does the parsimony tree and further suggests that high levels of homoplasy caused parsimony to underestimate the true extent of those trends. Simulations based on the character data and fossil record of hyaenids suggest that the maximum likelihood method is better able to estimate correct trees than is parsimony and somewhat better able to do so than previously proposed phylogenetic methods incorporating stratigraphy.

A new kumaraswamy generalized family of distributions: Properties and applications

2020 ◽  
Vol 70 (6) ◽  
pp. 1491-1510
Author(s):  
Muhammad Adnan Hussain ◽  
Muhammad Hussain Tahir ◽  
Gauss M. Cordeiro
Keyword(s):  
Maximum Likelihood ◽  
Real Life ◽  
Linear Representation ◽  
Maximum Likelihood Estimates ◽  
Data Sets ◽  
Modern Distribution ◽  
Real Life Data ◽  
Proposed Model ◽  
Method Of Maximum Likelihood ◽  
Family Of Distributions

AbstractThe Kumaraswamy generalized family of distributions proposed by Cordeiro and de-Castro (2011), has received increased attention in modern distribution theory with 624 google citations, and more than 50 special models have been studied so far. We define another generator, and then propose a new Kumaraswamy generalized family of distributions by inducting this new generator. Some useful properties of the proposed family are obtained such as quantiles, linear representation of the density, moments and generating function. The method of maximum likelihood is used for estimating family parameters. The properties of a special model of the family, called new Kumaraswamy-Burr XII distribution, are reported. A simulation study is conducted to assess the performance of maximum likelihood estimates of the proposed model. Two real-life data sets are analyzed to illustrate the flexibility of proposed model.

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