scholarly journals Non Bayesian estimation for survival and hazard function of weighted Rayleigh distribution (b)

2020 ◽  
pp. 3059-3071
Author(s):  
Saad Adnan Zain
Keyword(s):  
Hazard Function ◽  
Shape Parameter ◽  
Survival Function ◽  
Real Data ◽  
Rayleigh Distribution ◽  
Likelihood Method ◽  
Data Sets ◽  
New Class ◽  
The Moment ◽  
Two Parameters

In this paper, we proposed a new class of Weighted Rayleigh Distribution based on two parameters, one is scale parameter and the other is shape parameter which introduced in Rayleigh distribution. The main properties of this class are derived and investigated in . The moment method and maximum likelihood method are used to obtain estimators of parameters, survival function and hazard function. Real data sets are collected to investigate two methods which depend it in this study. A comparison was made between two methods of estimation.

scholarly journals The Censored Beta-Skew Alpha-Power Distribution

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1114
Author(s):  
Guillermo Martínez-Flórez ◽  
Roger Tovar-Falón ◽  
María Martínez-Guerra
Keyword(s):  
Power Distribution ◽  
Information Matrix ◽  
Real Data ◽  
Likelihood Method ◽  
Data Sets ◽  
Alpha Power ◽  
Score Functions ◽  
New Family ◽  
Two Parameters ◽  
Family Of Distributions

This paper introduces a new family of distributions for modelling censored multimodal data. The model extends the widely known tobit model by introducing two parameters that control the shape and the asymmetry of the distribution. Basic properties of this new family of distributions are studied in detail and a model for censored positive data is also studied. The problem of estimating parameters is addressed by considering the maximum likelihood method. The score functions and the elements of the observed information matrix are given. Finally, three applications to real data sets are reported to illustrate the developed methodology.

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 Type II General Exponential Class of Distributions

2019 ◽  
pp. 503-523 ◽  
Author(s):  
G. G. Hamedani ◽  
Mahdi Rasekhi ◽  
Sayed Najibi ◽  
Haitham M. Yousof ◽  
Morad Alizadeh
Keyword(s):  
Hazard Function ◽  
Residual Life ◽  
Real Data ◽  
Random Variable ◽  
Reliability Function ◽  
Interval Length ◽  
Data Sets ◽  
Type Ii ◽  
Mean Squared Errors ◽  
New Class

In this paper, a new class of continuous distributions with two extra positive parameters is introduced and is called the Type II General Exponential (TIIGE) distribution. Some special models are presented. Asymptotics, explicit expressions for the ordinary and incomplete moments, moment residual life, reversed residual life, quantile and generating functions and stress-strengh reliability function are derived. Characterizations of this family are obtained based on truncated moments, hazard function, conditional expectation of certain functions of the random variable are obtained. The performance of the maximum likelihood estimators in terms of biases, mean squared errors and confidence interval length is examined by means of a simulation study. Two real data sets are used to illustrate the application of the proposed class.

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 On The Transmuted Powered Moment Exponential Distribution

2021 ◽  
pp. 32-46
Author(s):  
Zafar Iqbal ◽  
Muhammad Rashad ◽  
Abdur Razaq ◽  
Muhammad Salman ◽  
Afsheen Javed
Keyword(s):  
Maximum Likelihood ◽  
Exponential Distribution ◽  
Survival Function ◽  
Likelihood Estimation ◽  
Real Data ◽  
Quantile Function ◽  
Rate Function ◽  
Data Sets ◽  
Inequality Measures ◽  
New Class

We introduce a new class of lifetime models called the transmuted powered moment exponential distribution. More specifically, the transmuted powered moment exponential distribution covers several new distributions. Survival analysis including survival function, hazard rate function and other related measures are computed. Analytical expressions for various mathematical properties of TPMED including rth moment, quantile function, inequality measures, and parameters are estimated by using maximum likelihood estimation and order statistics are also derived. A simulation study of the proposed distribution is performed. It is discovered that the Maximum Likelihood Estimators are consistent since the bias and Mean Square Error approach to zero when the sample size increases. The usefulness of the model associated with this distribution is illustrated by two real data sets and the new model provides a better fit than the models provided in literature.

scholarly journals Estimating of Survival Function under Type One Censoring Sample for Mixture Distribution

2020 ◽  
Vol 33 (4) ◽  
pp. 102
Author(s):  
Qesma S. Abadi ◽  
Iden H. AL-Kanani
Keyword(s):  
Probability Density Function ◽  
Censored Data ◽  
Hazard Function ◽  
Shape Parameter ◽  
Survival Function ◽  
Mixture Distribution ◽  
Real Data ◽  
Likelihood Estimator ◽  
Censored Sample ◽  
Newton Raphson

In this article, it is interesting to estimate and derive the three parameters which contain two scales parameters and one shape parameter of a new mixture distribution for the singly type one censored data which is the branch of right censored sample. Then to define some special mathematical and statistical properties for this new mixture distribution which is considered one of the continuous distributions characterized by its flexibility. Next,  using maximum likelihood estimator method for singly type one censored data based on the Newton-Raphson matrix procedure to find and estimate values of these three parameter by utilizing the real data taken from the National Center for Research and Treatment of Hematology/University of Mustansiriyah for leukemia diseases. After that we find and derive the estimate of probability density function, estimate survival function and finally estimate the hazard function. 

scholarly journals Marshall-Olkin Alpha Power Rayleigh Distribution: Properties, Characterizations, Estimation and Engineering applications

2021 ◽  
pp. 745-760
Author(s):  
Ehab Mohamed Almetwally ◽  
Ahmed Z. Afify ◽  
G. G. Hamedani
Keyword(s):  
Maximum Likelihood ◽  
Hazard Function ◽  
Real Data ◽  
Rayleigh Distribution ◽  
Estimation Methods ◽  
Data Sets ◽  
Alpha Power ◽  
Monte Carlo Simulation Study ◽  
Bootstrap Estimation ◽  
Proposed Model

In this paper, we introduce a new there-parameter Rayleigh distribution, called the Marshall-Olkin alpha power Rayleigh (MOAPR) distribution. Some statistical properties of the MOAPR distribution are obtained. The proposed model is characterized based on truncated moments and reverse hazard function. The maximum likelihood and bootstrap estimation methods are considered to estimate the MOPAR parameters. A Monte Carlo simulation study is performed to compare the maximum likelihood and bootstrap estimation methods. Superiority of the MOAPR distribution over some well-known distributions is illustrated by means of two real data sets.

scholarly journals Properties and Inference for a New Class of Generalized Rayleigh Distributions with an Application

2019 ◽  
Vol 17 (1) ◽  
pp. 700-715
Author(s):  
Hayrinisa Demirci Biçer
Keyword(s):  
Survival Function ◽  
Real Data ◽  
Rayleigh Distribution ◽  
Least Square ◽  
Statistical Characteristics ◽  
Data Sets ◽  
Alpha Power ◽  
Inference Problem ◽  
Proposed Model ◽  
Generalized Rayleigh Distribution

Abstract In the present paper, we introduce a new form of generalized Rayleigh distribution called the Alpha Power generalized Rayleigh (APGR) distribution by following the idea of extension of the distribution families with the Alpha Power transformation. The introduced distribution has the more general form than both the Rayleigh and generalized Rayleigh distributions and provides a better fit than the Rayleigh and generalized Rayleigh distributions for more various forms of the data sets. In the paper, we also obtain explicit forms of some important statistical characteristics of the APGR distribution such as hazard function, survival function, mode, moments, characteristic function, Shannon and Rényi entropies, stress-strength probability, Lorenz and Bonferroni curves and order statistics. The statistical inference problem for the APGR distribution is investigated by using the maximum likelihood and least-square methods. The estimation performances of the obtained estimators are compared based on the bias and mean square error criteria by a conducted Monte-Carlo simulation on small, moderate and large sample sizes. Finally, a real data analysis is given to show how the proposed model works in practice.

scholarly journals A New One-parameter G Family of Compound Distributions: Copulas, Statistical Properties and Applications

2021 ◽  
Vol 9 (4) ◽  
pp. 942-962
Author(s):  
Mohamed Abo Raya
Keyword(s):  
Maximum Likelihood ◽  
Hazard Function ◽  
Maximum Likelihood Method ◽  
Real Data ◽  
Heavy Tail ◽  
Statistical Properties ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Sets ◽  
New Family

This work introduces a new one-parameter compound G family. Relevant statistical properties are derived. The new density can be “asymmetric right skewed with one peak and a heavy tail”, “symmetric” and “left skewedwith one peak”. The new hazard function can be “upside-down”, “upside-down-constant”, “increasing”, “decreasing” and “decreasing-constant”. Many bivariate types have been also derived via different common copulas. The estimation of the model parameters is performed by maximum likelihood method. The usefulness and flexibility of the new family is illustrated by means of two real data sets.

scholarly journals Alpha-Power Exponentiated Inverse Rayleigh distribution and its applications to real and simulated data

PLoS ONE ◽  
2021 ◽  
Vol 16 (1) ◽  
pp. e0245253
Author(s):  
Muhammad Ali ◽  
Alamgir Khalil ◽  
Muhammad Ijaz ◽  
Noor Saeed
Keyword(s):  
Residual Life ◽  
Probability Distributions ◽  
Simulated Data ◽  
Real Data ◽  
Rayleigh Distribution ◽  
Likelihood Method ◽  
Strength Parameter ◽  
Data Sets ◽  
Alpha Power ◽  
Mean Waiting Time

The main goal of the current paper is to contribute to the existing literature of probability distributions. In this paper, a new probability distribution is generated by using the Alpha Power Family of distributions with the aim to model the data with non-monotonic failure rates and provides a better fit. The proposed distribution is called Alpha Power Exponentiated Inverse Rayleigh or in short APEIR distribution. Various statistical properties have been investigated including they are the order statistics, moments, residual life function, mean waiting time, quantiles, entropy, and stress-strength parameter. To estimate the parameters of the proposed distribution, the maximum likelihood method is employed. It has been proved theoretically that the proposed distribution provides a better fit to the data with monotonic as well as non-monotonic hazard rate shapes. Moreover, two real data sets are used to evaluate the significance and flexibility of the proposed distribution as compared to other probability distributions.

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