scholarly journals Statistical Properties & Different Methods Of Estimation Of A New Extended Weighted Frechet Distribution.

2021 ◽  
Vol 12 (6) ◽  
pp. 1011-1029
Author(s):  
Mahdi Wahhab Neamah , Et. al.
Keyword(s):  
Statistical Properties ◽  
Likelihood Method ◽  
Estimation Methods ◽  
Percentile Method ◽  
Fréchet Distribution ◽  
Coefficients Of Variation ◽  
Coefficient Of Skewness ◽  
Frechet Distribution ◽  
Mean Variance ◽  
New Distribution

In this paper, we introduce a new distribution is called the extended weighted Frechet distribution, which we obtain by applying the Azzalini method and deduced some statistical properties such as mean, variance, coefficients of variation, coefficient of skewness, and coefficient of kurtosis. The parameters of the new distribution were estimated by the following estimation methods: Maximum Likelihood Method (MLE) and percentile method. We used the Monte Carlo simulation to compare the performances of the proposed estimators obtained through methods of estimation.

Properties and methods of estimation for a bivariate exponentiated Fréchet distribution

2020 ◽  
Vol 70 (5) ◽  
pp. 1211-1230
Author(s):  
Abdus Saboor ◽  
Hassan S. Bakouch ◽  
Fernando A. Moala ◽  
Sheraz Hussain
Keyword(s):  
Maximum Likelihood ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Superior Performance ◽  
Estimation Methods ◽  
Conditional Probability Density ◽  
Data Set ◽  
Fréchet Distribution ◽  
Frechet Distribution

AbstractIn this paper, a bivariate extension of exponentiated Fréchet distribution is introduced, namely a bivariate exponentiated Fréchet (BvEF) distribution whose marginals are univariate exponentiated Fréchet distribution. Several properties of the proposed distribution are discussed, such as the joint survival function, joint probability density function, marginal probability density function, conditional probability density function, moments, marginal and bivariate moment generating functions. Moreover, the proposed distribution is obtained by the Marshall-Olkin survival copula. Estimation of the parameters is investigated by the maximum likelihood with the observed information matrix. In addition to the maximum likelihood estimation method, we consider the Bayesian inference and least square estimation and compare these three methodologies for the BvEF. A simulation study is carried out to compare the performance of the estimators by the presented estimation methods. The proposed bivariate distribution with other related bivariate distributions are fitted to a real-life paired data set. It is shown that, the BvEF distribution has a superior performance among the compared distributions using several tests of goodness–of–fit.

scholarly journals A Distribution for Instantaneous Failures

Stats ◽  
2019 ◽  
Vol 2 (2) ◽  
pp. 247-258 ◽  
Author(s):  
Pedro L. Ramos ◽  
Francisco Louzada
Keyword(s):  
Residual Life ◽  
Likelihood Estimation ◽  
Estimation Methods ◽  
Mean Residual Life ◽  
Parameter Distribution ◽  
Coverage Probabilities ◽  
Instantaneous Failures ◽  
The Relationship ◽  
Mean Variance ◽  
New Distribution

A new one-parameter distribution is proposed in this paper. The new distribution allows for the occurrence of instantaneous failures (inliers) that are natural in many areas. Closed-form expressions are obtained for the moments, mean, variance, a coefficient of variation, skewness, kurtosis, and mean residual life. The relationship between the new distribution with the exponential and Lindley distributions is presented. The new distribution can be viewed as a combination of a reparametrized version of the Zakerzadeh and Dolati distribution with a particular case of the gamma model and the occurrence of zero value. The parameter estimation is discussed under the method of moments and the maximum likelihood estimation. A simulation study is performed to verify the efficiency of both estimation methods by computing the bias, mean squared errors, and coverage probabilities. The superiority of the proposed distribution and some of its concurrent distributions are tested by analyzing four real lifetime datasets.

scholarly journals Transmuted Mukherjee-Islam Distribution: A Generalization of Mukherjee-Islam Distribution

2017 ◽  
Vol 9 (4) ◽  
pp. 135
Author(s):  
Loai M. A. Al-Zou'bi
Keyword(s):  
Hazard Rate ◽  
Maximum Likelihood Method ◽  
Continuous Distribution ◽  
Quantile Function ◽  
Descriptive Statistics ◽  
Likelihood Method ◽  
Distribution Parameters ◽  
Rate Functions ◽  
Mean Variance ◽  
New Distribution

A new continuous distribution is proposed in this paper. This distribution is a generalization of Mukherjee-Islam distribution using the quadratic rank transmutation map. It is called transmuted Mukherjee-Islam distribution (TMID). We have studied many properties of the new distribution: Reliability and hazard rate functions. The descriptive statistics: mean, variance, skewness, kurtosis are also studied. Maximum likelihood method is used to estimate the distribution parameters. Order statistics and Renyi and Tsallis entropies were also calculated. Furthermore, the quantile function and the median are calculated.

scholarly journals Two-Parameter Nwikpe (TPAN) Distribution with Application

2021 ◽  
pp. 56-67
Author(s):  
Barinaadaa John Nwikpe ◽  
Isaac Didi Essi
Keyword(s):  
Goodness Of Fit ◽  
Continuous Distribution ◽  
Real Life ◽  
Moment Generating Function ◽  
Statistical Properties ◽  
Likelihood Method ◽  
Data Sets ◽  
Method Of Moment ◽  
Two Parameter ◽  
New Distribution

A new two-parameter continuous distribution called the Two-Parameter Nwikpe (TPAN) distribution is derived in this paper. The new distribution is a mixture of gamma and exponential distributions. A few statistical properties of the new probability distribution have been derived. The shape of its density for different values of the parameters has also been established.  The first four crude moments, the second and third moments about the mean of the new distribution were derived using the method of moment generating function. Other statistical properties derived include; the distribution of order statistics, coefficient of variation and coefficient of skewness. The parameters of the new distribution were estimated using maximum likelihood method. The flexibility of the Two-Parameter Nwikpe (TPAN) distribution was shown by fitting the distribution to three real life data sets. The goodness of fit shows that the new distribution outperforms the one parameter exponential, Shanker and Amarendra distributions for the data sets used for this study.

scholarly journals A New Three-parameter Xgamma Fréchet Distribution with Different Methods of Estimation and Applications

2021 ◽  
pp. 291-308
Author(s):  
Mohamed Ibrahim Mohamed ◽  
Laba Handique ◽  
Subrata Chakraborty ◽  
Nadeem Shafique Butt ◽  
Haitham M. Yousof
Keyword(s):  
Real Life ◽  
Estimation Methods ◽  
Data Sets ◽  
Clear Preference ◽  
Life Data ◽  
Fréchet Distribution ◽  
Real Life Data ◽  
Proposed Model ◽  
Frechet Distribution

In this article an attempt is made to introduce a new extension of the Fréchet model called the Xgamma Fréchet model. Some of its properties are derived. The estimation of the parameters via different estimation methods are discussed. The performances of the proposed estimation methods are investigated through simulations as well as real life data sets. The potentiality of the proposed model is established through modelling of two real life data sets. The results have shown clear preference for the proposed model compared to several know competing ones.

scholarly journals An extensive extension of exponentiated exponential distribution using alpha power transformation – statistical properties and applications in engineering science

2021 ◽  
Vol 17 (2) ◽  
pp. 59-74
Author(s):  
S. Qurat Ul Ain ◽  
K. Ul Islam Rather
Keyword(s):  
Exponential Distribution ◽  
Real Life ◽  
Statistical Properties ◽  
Data Sets ◽  
Alpha Power ◽  
Real Life Data ◽  
Proposed Model ◽  
Mean Variance ◽  
New Distribution ◽  
Extra Parameter

Abstract In this article, an extension of exponentiated exponential distribution is familiarized by adding an extra parameter to the parent distribution using alpha power technique. The new distribution obtained is referred to as Alpha Power Exponentiated Exponential Distribution. Various statistical properties of the proposed distribution like mean, variance, central and non-central moments, reliability functions and entropies have been derived. Two real life data sets have been applied to check the flexibility of the proposed model. The new density model introduced provides the better fit when compared with other related statistical models.

scholarly journals Estimation of Constant Stress Partially Accelerated Life Test for Fréchet Distribution with Type-I Censoring

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Abdullah Ali H. Ahmadini ◽  
Wali Khan Mashwani ◽  
Rehman Ahmad Khan Sherwani ◽  
Shokrya S. Alshqaq ◽  
Farrukh Jamal ◽  
...  
Keyword(s):  
Constant Stress ◽  
Accelerated Life Test ◽  
Likelihood Method ◽  
Type I ◽  
Type I Censoring ◽  
Fréchet Distribution ◽  
Accelerated Life Tests ◽  
Accelerated Life ◽  
Life Tests ◽  
Frechet Distribution

Modern reliability engineering accelerated life tests (ALT) and partially accelerated life tests (PALT) are widely used to obtain the timely information on the reliability of objects, products, elements, and materials as well as to save time and cost. The ALTs or PALTs are useful in determining the failed manners of the items at routine conditions by using the information of the data generated from the experiment. PALT is the most sensible method to be used for estimating both ordinary and ALTs. In this research, constant stress PALT design for the Fréchet distribution with type-I censoring has been investigated due to a wide applicability of the Fréchet distribution in engineering problems especially in hydrology. The distribution parameters and acceleration factor are obtained by using the maximum likelihood method. Fisher's information matrix is used to develop the asymptotic confidence interval estimates of the model parameters. A simulation study is conducted to illustrate the statistical properties of the parameters and the confidence intervals by using the R software. The results indicated that the constant stress PALT plan works well. Moreover, a numerical example is given to exemplify the performance of the proposed methods.

scholarly journals A New Version of the Exponentiated Exponential Distribution: Copula, Properties and Application to Relief and Survival Times

2021 ◽  
Vol 9 (2) ◽  
pp. 311-333
Author(s):  
Hanaa Elgohari
Keyword(s):  
Exponential Distribution ◽  
Hazard Function ◽  
Real Data ◽  
Likelihood Method ◽  
Type Model ◽  
Data Sets ◽  
Survival Times ◽  
Mathematical Properties ◽  
Mean Variance ◽  
New Distribution

In this paper, we introduce a new generalization of the Exponentiated Exponential distribution. Various structural mathematical properties are derived. Numerical analysis for mean, variance, skewness and kurtosis and the dispersion index is performed. The new density can be right skewed and symmetric with "unimodal" and "bimodal" shapes. The new hazard function can be "constant", "decreasing", "increasing", "increasing-constant", "upside down-constant", "decreasing nstant". Many bivariate and multivariate type model have been also derived. We assess the performance of the maximum likelihood method graphically via the biases and mean squared errors. The usefulness and flexibility of the new distribution is illustrated by means of two real data sets.

scholarly journals Nwikpe Probability Distribution: Statistical Properties and Goodness of Fit

2021 ◽  
pp. 52-61
Author(s):  
Barinaadaa John Nwikpe ◽  
Isaac, Didi Essi ◽  
Amos Emeka
Keyword(s):  
Probability Distribution ◽  
Goodness Of Fit ◽  
Real Life ◽  
Moment Generating Function ◽  
Statistical Properties ◽  
Likelihood Method ◽  
Data Sets ◽  
The Moment ◽  
The One ◽  
New Distribution

In this paper, we introduce a new continuous probability distribution developed from two classical distributions namely, gamma and exponential distributions. The new distribution is called the Nwikpe distribution. Some statistical properties of the new distribution were derived. The shapes of its probability density function have been established for different values of the parameters.  The moment generating function, the first four raw moments, the second moment about the mean, Renyi’s entropy and the distribution of order statistics were derived. The parameter of the new distribution was estimated using maximum likelihood method. The shape of the hazard function of the new distribution is increasing. The flexibility of the distribution was shown using some real life data sets, the goodness of fit shows that the new distribution gives a better fit to the data sets used in this study than the one parameter exponential, Shanker, Lindley, Akash, Sujatha and Amarendra distributions.

Sign in / Sign up

Export Citation Format

Share Document