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 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 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 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 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 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.

scholarly journals An alternative Laplace distribution

2020 ◽  
Vol 53 (2) ◽  
pp. 111-127
Author(s):  
C. Satheesh Kumar ◽  
Rosmi Jose
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Simulation Study ◽  
Real Life ◽  
Likelihood Estimation ◽  
Laplace Distribution ◽  
Data Sets ◽  
Life Data ◽  
Real Life Data ◽  
Alternative Version

In this paper, we propose an alternative version to the Laplace distribution which we named as “alternative Laplace distribution (ALD)” and discuss some of its important properties. A location-scale extension of the ALD is considered and the maximum likelihood estimation procedures for estimating its parameters is described. Further, the distribution is fitted to certain real life data sets for illustrating the utility of the model. A simulation study is carried out to examine the performance of likelihood estimators of the parameters of the distribution.

scholarly journals On the Mistaken Use of the Chi-Square Test in Benford’s Law

Stats ◽  
2021 ◽  
Vol 4 (2) ◽  
pp. 419-453
Author(s):  
Alex Ely Kossovsky
Keyword(s):  
Research Question ◽  
Real Life ◽  
Benford’S Law ◽  
Data Sets ◽  
Chi Square ◽  
Data Set ◽  
Life Data ◽  
Real Life Data ◽  
Benford's Law ◽  
Chi Square Test

Benford’s Law predicts that the first significant digit on the leftmost side of numbers in real-life data is distributed between all possible 1 to 9 digits approximately as in LOG(1 + 1/digit), so that low digits occur much more frequently than high digits in the first place. Typically researchers, data analysts, and statisticians, rush to apply the chi-square test in order to verify compliance or deviation from this statistical law. In almost all cases of real-life data this approach is mistaken and without mathematical-statistics basis, yet it had become a dogma or rather an impulsive ritual in the field of Benford’s Law to apply the chi-square test for whatever data set the researcher is considering, regardless of its true applicability. The mistaken use of the chi-square test has led to much confusion and many errors, and has done a lot in general to undermine trust and confidence in the whole discipline of Benford’s Law. This article is an attempt to correct course and bring rationality and order to a field which had demonstrated harmony and consistency in all of its results, manifestations, and explanations. The first research question of this article demonstrates that real-life data sets typically do not arise from random and independent selections of data points from some larger universe of parental data as the chi-square approach supposes, and this conclusion is arrived at by examining how several real-life data sets are formed and obtained. The second research question demonstrates that the chi-square approach is actually all about the reasonableness of the random selection process and the Benford status of that parental universe of data and not solely about the Benford status of the data set under consideration, since the focus of the chi-square test is exclusively on whether the entire process of data selection was probable or too rare. In addition, a comparison of the chi-square statistic with the Sum of Squared Deviations (SSD) measure of distance from Benford is explored in this article, pitting one measure against the other, and concluding with a strong preference for the SSD measure.

scholarly journals Calibration-Based Estimators using Different Distance Measures under Two Auxiliary Variables: A Comparative Study

2021 ◽  
Vol 19 (1) ◽  
pp. 2-20
Author(s):  
Piyush Kant Rai ◽  
Alka Singh ◽  
Muhammad Qasim
Keyword(s):  
Mean Squared Error ◽  
Real Life ◽  
Distance Functions ◽  
Distance Measures ◽  
Auxiliary Variables ◽  
Data Set ◽  
Life Data ◽  
Squared Error ◽  
Real Life Data ◽  
Relative Root

This article introduces calibration estimators under different distance measures based on two auxiliary variables in stratified sampling. The theory of the calibration estimator is presented. The calibrated weights based on different distance functions are also derived. A simulation study has been carried out to judge the performance of the proposed estimators based on the minimum relative root mean squared error criterion. A real-life data set is also used to confirm the supremacy of the proposed method.

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.

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