scholarly journals The Marshall-Olkin Extended Gumbel-weibull Distribution: Properties And Applications

2021 ◽  
Vol 16 (1) ◽  
pp. 2603-2627
Author(s):  
Elebe Emmanuel Nwezza ◽  
Fidelis Ifeanyi Ugwuowo
Keyword(s):  
Maximum Likelihood ◽  
Real Life ◽  
Estimation Method ◽  
Quantile Function ◽  
Lifetime Distribution ◽  
Maximum Likelihood Estimates ◽  
Simulation Studies ◽  
Test Statistics ◽  
Maximum Likeli ◽  
New Distribution

We introduce a new lifetime distribution called Marshall-Olkin extended Gumbel-Weibull. Some properties of distribution such as moments, TL-moments, quantile function, en- tropy, and order statistics are studied. The fexibility of the distribution to model unimodal, monotone shapes as well as unimodal, bimodal, monotone failure rates are presented. The estimators of the parameters of the distribution were obtained using the maximum likeli- hood estimation method. The performance of the maximum likelihood estimates of the Marshall-Olkin extended Gumbel-Weibulll parameters was observed through simulation studies. Two real life applications to illustrate the potentials of the new distribution are presented, and comparison with other distribution having the same baseline is done using goodness-of-test statistics.

scholarly journals A New Extension of Quasi Lindley Distribution: Properties and Applications

2019 ◽  
Vol 7 (2) ◽  
pp. 28
Author(s):  
Patrick Udoudo Unyime ◽  
Ette Harrison Etuk
Keyword(s):  
Maximum Likelihood ◽  
Estimation Method ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Point Estimation ◽  
Maximum Likelihood Estimates ◽  
Lindley Distribution ◽  
Likelihood Point ◽  
Point Estimation Method ◽  
New Distribution

In this paper, we introduced and studied the statistical properties of a new distribution called the Marshall-Olkin extended quasi Lindley distribution. Specifically, we derived the crude moment, moment generating function, quantile function, and distributions of order statisticsbased on the distribution. The maximum likelihood point estimation method was used to estimate the parameters of the newly introduced model. Some AR minfication processes were discussed. We illustrated the applicability of the distribution using a real dataset.Keywords: Marshal-Olkin family of distributions; maximum likelihood estimates; minification processes; quasi Lindley distribution; quantile function.

scholarly journals E-Bayesian Estimation Based on Burr-X Generalized Type-II Hybrid Censored Data

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 626
Author(s):  
Abdalla Rabie ◽  
Junping Li
Keyword(s):  
Maximum Likelihood ◽  
Bayesian Estimation ◽  
Real Life ◽  
Estimation Method ◽  
Reliability Function ◽  
Maximum Likelihood Estimates ◽  
Estimation Methods ◽  
Type Ii ◽  
Credible Intervals ◽  
Generalized Type

In this article, we are concerned with the E-Bayesian (the expectation of Bayesian estimate) method, the maximum likelihood and the Bayesian estimation methods of the shape parameter, and the reliability function of one-parameter Burr-X distribution. A hybrid generalized Type-II censored sample from one-parameter Burr-X distribution is considered. The Bayesian and E-Bayesian approaches are studied under squared error and LINEX loss functions by using the Markov chain Monte Carlo method. Confidence intervals for maximum likelihood estimates, as well as credible intervals for the E-Bayesian and Bayesian estimates, are constructed. Furthermore, an example of real-life data is presented for the sake of the illustration. Finally, the performance of the E-Bayesian estimation method is studied then compared with the performance of the Bayesian and maximum likelihood methods.

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 Generalized Lindley-Quasi Xgamma distribution

2021 ◽  
Vol 17 (1) ◽  
pp. 5-30
Author(s):  
S. A. Wani ◽  
S. Shafi
Keyword(s):  
Maximum Likelihood ◽  
Goodness Of Fit ◽  
Real Life ◽  
Estimation Method ◽  
Maximum Likelihood Estimates ◽  
Ratio Test ◽  
Life Data ◽  
Weight Parameter ◽  
Real Life Data ◽  
Proposed Model

Abstract We obtained a new generalization of Lindley-Quasi Xgamma distribution by adding weight parameter to it through weighting technique and have shown the flexibility of proposed model. Expression for reliability measures, order statistics, Bonferroni curves & indices, Renyi entropy along with some other important properties are derived. Maximum likelihood estimation method is put to use for estimation of unknown parameters of proposed model. Simulation study for checking the performance of maximum likelihood estimates and for model comparison is carried out. Proposed model and its related models are fitted to real life data sets and goodness of fit measure Kolmogorov statistic & p-value, loss of information criteria’s AIC, BIC, AICC & HQIC are computed through R software to check the applicability of proposed model in real life. The significance of weight parameter is also tested by using likelihood ratio test for both randomly generated data as well as real life data.

scholarly journals Sine Inverse Lomax Generated Family of Distributions with Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Aisha Fayomi ◽  
Ali Algarni ◽  
Abdullah M. Almarashi
Keyword(s):  
Maximum Likelihood ◽  
Real Life ◽  
Likelihood Estimation ◽  
Quantile Function ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
New Family ◽  
Estimation Of Model Parameters ◽  
Generated Family ◽  
Family Of Distributions

This paper introduces a new family of distributions by combining the sine produced family and the inverse Lomax generated family. The new proposed family is very interested and flexible more than some old and current families. It has many new models which have many applications in physics, engineering, and medicine. Some fundamental statistical properties of the sine inverse Lomax generated family of distributions as moments, generating function, and quantile function are calculated. Four special models as sine inverse Lomax-exponential, sine inverse Lomax-Rayleigh, sine inverse Lomax-Frèchet and sine inverse Lomax-Lomax models are proposed. Maximum likelihood estimation of model parameters is proposed in this paper. For the purpose of evaluating the performance of maximum likelihood estimates, a simulation study is conducted. Two real life datasets are analyzed by the sine inverse Lomax-Lomax model, and we show that providing flexibility and more fitting than known nine models derived from other generated families.

scholarly journals The Weibull Birnbaum-Saunders Distribution And Its Applications

2020 ◽  
Vol 9 (1) ◽  
pp. 61-81
Author(s):  
Lazhar BENKHELIFA
Keyword(s):  
Maximum Likelihood ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Reliability Estimation ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Data Sets ◽  
Proposed Model ◽  
Modeling Data

A new lifetime model, with four positive parameters, called the Weibull Birnbaum-Saunders distribution is proposed. The proposed model extends the Birnbaum-Saunders distribution and provides great flexibility in modeling data in practice. Some mathematical properties of the new distribution are obtained including expansions for the cumulative and density functions, moments, generating function, mean deviations, order statistics and reliability. Estimation of the model parameters is carried out by the maximum likelihood estimation method. A simulation study is presented to show the performance of the maximum likelihood estimates of the model parameters. The flexibility of the new model is examined by applying it to two real data sets.

scholarly journals On Modified Burr XII-Inverse Weibull Distribution: Development, Properties, Characterizations and Applications

2020 ◽  
pp. 721-735
Author(s):  
Fiaz Ahmad Bhatti ◽  
G. G. Hamedani ◽  
Haitham M. Yousof ◽  
Azeem Ali ◽  
Munir Ahmad
Keyword(s):  
Maximum Likelihood ◽  
Hazard Rate ◽  
Maximum Likelihood Method ◽  
Real Data ◽  
Lifetime Distribution ◽  
Maximum Likelihood Estimates ◽  
Likelihood Method ◽  
Data Sets ◽  
Quarterly Earnings ◽  
Inverse Weibull Distribution

A flexible lifetime distribution with increasing, decreasing, inverted bathtub and modified bathtub hazard rate called Modified Burr XII-Inverse Weibull (MBXII-IW) is introduced and studied. The density function of MBXII-IW is exponential, left-skewed, right-skewed and symmetrical shaped.  Descriptive measures on the basis of quantiles, moments, order statistics and reliability measures are theoretically established. The MBXII-IW distribution is characterized via different techniques. Parameters of MBXII-IW distribution are estimated using maximum likelihood method. The simulation study is performed to illustrate the performance of the maximum likelihood estimates (MLEs). The potentiality of MBXII-IW distribution is demonstrated by its application to real data sets: serum-reversal times and quarterly earnings.

scholarly journals The Exponentiated Gumbel Type-2 Distribution: Properties and Application

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
I. E. Okorie ◽  
A. C. Akpanta ◽  
J. Ohakwe
Keyword(s):  
Lifetime Distribution ◽  
The Other ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Lifetime Data ◽  
Data Set ◽  
Method Of Maximum Likelihood ◽  
Log Likelihood ◽  
New Distribution

We introduce a generalized version of the standard Gumble type-2 distribution. The new lifetime distribution is called the Exponentiated Gumbel (EG) type-2 distribution. The EG type-2 distribution has three nested submodels, namely, the Gumbel type-2 distribution, the Exponentiated Fréchet (EF) distribution, and the Fréchet distribution. Some statistical and reliability properties of the new distribution were given and the method of maximum likelihood estimates was proposed for estimating the model parameters. The usefulness and flexibility of the Exponentiated Gumbel (EG) type-2 distribution were illustrated with a real lifetime data set. Results based on the log-likelihood and information statistics values showed that the EG type-2 distribution provides a better fit to the data than the other competing distributions. Also, the consistency of the parameters of the new distribution was demonstrated through a simulation study. The EG type-2 distribution is therefore recommended for effective modelling of lifetime data.

scholarly journals A New Generalized Transmuted Inverse Exponential Distribution: Properties and Application

2018 ◽  
pp. 1-13
Author(s):  
Uchenna U. Uwadi ◽  
Elebe E. Nwaezza
Keyword(s):  
Exponential Distribution ◽  
Real Life ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Maximum Likelihood Estimates ◽  
Data Set ◽  
Real Life Data ◽  
Proposed Model ◽  
Inverse Exponential Distribution ◽  
The Moment

In this study, we proposed a new generalised transmuted inverse exponential distribution with three parameters and have transmuted inverse exponential and inverse exponential distributions as sub models. The hazard function of the distribution is nonmonotonic, unimodal and inverted bathtub shaped making it suitable for modelling lifetime data. We derived the moment, moment generating function, quantile function, maximum likelihood estimates of the parameters, Renyi entropy and order statistics of the distribution. A real life data set is used to illustrate the usefulness of the proposed model.     

scholarly journals The Gompertz Gumbel II Distribution: Properties and Applications

2020 ◽  
pp. 1-15
Author(s):  
Adebisi Ade Ogunde ◽  
Gbenga Adelekan Olalude ◽  
Donatus Osaretin Omosigho
Keyword(s):  
Real Life ◽  
Stochastic Ordering ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Data Sets ◽  
Monte Carlo Simulation Study ◽  
Life Data ◽  
Real Life Data ◽  
Decreasing Failure Rate ◽  
New Distribution

In this paper we introduced Gompertz Gumbel II (GG II) distribution which generalizes the Gumbel II distribution. The new distribution is a flexible exponential type distribution which can be used in modeling real life data with varying degree of asymmetry. Unlike the Gumbel II distribution which exhibits a monotone decreasing failure rate, the new distribution is useful for modeling unimodal (Bathtub-shaped) failure rates which sometimes characterised the real life data. Structural properties of the new distribution namely, density function, hazard function, moments, quantile function, moment generating function, orders statistics, Stochastic Ordering, Renyi entropy were obtained. For the main formulas related to our model, we present numerical studies that illustrate the practicality of computational implementation using statistical software. We also present a Monte Carlo simulation study to evaluate the performance of the maximum likelihood estimators for the GGTT model. Three life data sets were used for applications in order to illustrate the flexibility of the new model.

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