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.

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 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 Generalization of the Lomax Distribution with Increasing, Decreasing, and Constant Failure Rate

2017 ◽  
Vol 2017 ◽  
pp. 1-6 ◽  
Author(s):  
Pelumi E. Oguntunde ◽  
Mundher A. Khaleel ◽  
Mohammed T. Ahmed ◽  
Adebowale O. Adejumo ◽  
Oluwole A. Odetunmibi
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Real Life ◽  
Likelihood Estimation ◽  
Model Parameters ◽  
Lomax Distribution ◽  
Life Data ◽  
Real Life Data ◽  
Method Of Maximum Likelihood ◽  
Better Than

Developing new compound distributions which are more flexible than the existing distributions have become the new trend in distribution theory. In this present study, the Lomax distribution was extended using the Gompertz family of distribution, its resulting densities and statistical properties were carefully derived, and the method of maximum likelihood estimation was proposed in estimating the model parameters. A simulation study to assess the performance of the parameters of Gompertz Lomax distribution was provided and an application to real life data was provided to assess the potentials of the newly derived distribution. Excerpt from the analysis indicates that the Gompertz Lomax distribution performed better than the Beta Lomax distribution, Weibull Lomax distribution, and Kumaraswamy Lomax distribution.

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 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 Hypothesis Testing on the Location Parameter of a Skew-Normal Distribution (SND) with Application

2018 ◽  
Vol 20 ◽  
pp. 03003
Author(s):  
Phontita Thiuthad ◽  
Nabendu Pal
Keyword(s):  
Normal Distribution ◽  
Real Life ◽  
Location Parameter ◽  
Test Methods ◽  
Skew Normal Distribution ◽  
Data Set ◽  
Sample Mean ◽  
Real Life Data ◽  
Approximate Probability ◽  
Skew Normal

This work deals with testing a hypothesis on the location parameter (μ) of a skew-normal distribution (SND) based on a random sample of size n. The details of this work can be summarized in four major components: (a) First we review some useful results on SND, including the approximate probability distribution of the sample average. (b) Next, we develop several tests to test a hypothesis on μ based on the sample mean when the scale (σ) and shape (λ) parameters are known. (c) The tests for the known scale and shape are then extended for unknown scale and shape. (d) Finally, the test methods have been used for a real-life data set.

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 Bayesian Analysis of Extended Cox Model with Time-Varying Covariates Using Bootstrap Prior

2020 ◽  
Vol 18 (2) ◽  
pp. 2-13
Author(s):  
Oyebayo Ridwan Olaniran ◽  
Mohd Asrul Affendi Abdullah
Keyword(s):  
Empirical Bayes ◽  
Cox Model ◽  
Real Life ◽  
Estimation Procedure ◽  
Time Varying ◽  
Data Set ◽  
Life Data ◽  
Real Life Data ◽  
Time Varying Covariates ◽  
Extended Cox Model

A new Bayesian estimation procedure for extended cox model with time varying covariate was presented. The prior was determined using bootstrapping technique within the framework of parametric empirical Bayes. The efficiency of the proposed method was observed using Monte Carlo simulation of extended Cox model with time varying covariates under varying scenarios. Validity of the proposed method was also ascertained using real life data set of Stanford heart transplant. Comparison of the proposed method with its competitor established appreciable supremacy of the method.

scholarly journals On Properties of the Bimodal Skew-Normal Distribution and an Application

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 703
Author(s):  
David Elal-Olivero ◽  
Juan F. Olivares-Pacheco ◽  
Osvaldo Venegas ◽  
Heleno Bolfarine ◽  
Héctor W. Gómez
Keyword(s):  
Maximum Likelihood ◽  
Normal Distribution ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Skew Normal Distribution ◽  
Data Set ◽  
Normal Distributions ◽  
Stochastic Representations ◽  
Skew Normal

The main object of this paper is to develop an alternative construction for the bimodal skew-normal distribution. The construction is based upon a study of the mixture of skew-normal distributions. We study some basic properties of this family, its stochastic representations and expressions for its moments. Parameters are estimated using the maximum likelihood estimation method. A simulation study is carried out to observe the performance of the maximum likelihood estimators. Finally, we compare the efficiency of the new distribution with other distributions in the literature using a real data set. The study shows that the proposed approach presents satisfactory results.

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