scholarly journals A New Modified Kies Family: Properties, Estimation Under Complete and Type-II Censored Samples, and Engineering Applications

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1345 ◽  
Author(s):  
Abdulhakim A. Al-Babtain ◽  
Mohammed K. Shakhatreh ◽  
Mazen Nassar ◽  
Ahmed Z. Afify
Keyword(s):  
Exponential Distribution ◽  
Real Life ◽  
Real Data ◽  
Mean Residual Life ◽  
Type Ii ◽  
Censored Samples ◽  
New Family ◽  
Generalized Distributions ◽  
Two Parameters ◽  
New Distribution

In this paper, we introduce a new family of continuous distributions that is called the modified Kies family of distributions. The main mathematical properties of the new family are derived. A special case of the new family has been considered in more detail; namely, the two parameters modified Kies exponential distribution with bathtub shape, decreasing and increasing failure rate function. The importance of the new distribution comes from its ability in modeling positively and negatively skewed real data over some generalized distributions with more than two parameters. The shape behavior of the hazard rate and the mean residual life functions of the modified Kies exponential distribution are discussed. We use the method of maximum likelihood to estimate the distribution parameters based on complete and type-II censored samples. The approximate confidence intervals are also obtained under the two schemes. A simulation study is conducted and two real data sets from the engineering field are analyzed to show the flexibility of the new distribution in modeling real life data.

scholarly journals Modeling Life Time Data by Generalized Weibull-generalized Exponential Distribution

2020 ◽  
pp. 65-75
Author(s):  
N. I. Badmus ◽  
Faweya, Olanrewaju
Keyword(s):  
Exponential Distribution ◽  
Information Matrix ◽  
Real Life ◽  
Likelihood Estimation ◽  
Life Time ◽  
Generalized Exponential Distribution ◽  
Time Data ◽  
Air Conditioning System ◽  
Generalized Distributions ◽  
New Distribution

This paper convolutes two generalized distributions from the family of generated T - X distribution. The new distribution generated from these distributions is called the Generalized Weibull-generalized Exponential Distribution. The properties of the proposed distribution are derived. Method of maximum likelihood estimation is used to estimate the parameters of the distribution and the information matrix is obtained. Thereafter, the distribution is applied to a real life dataset of failure for the air conditioning system and the obtained results are compared with other existing distributions to illustrate the capability and flexibility of the new distribution.

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 The modified beta transmuted family of distributions with applications using the exponential distribution

PLoS ONE ◽  
2021 ◽  
Vol 16 (11) ◽  
pp. e0258512
Author(s):  
Phillip Oluwatobi Awodutire ◽  
Oluwafemi Samson Balogun ◽  
Akintayo Kehinde Olapade ◽  
Ethelbert Chinaka Nduka
Keyword(s):  
Exponential Distribution ◽  
Real Life ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Life Time ◽  
Time Data ◽  
New Family ◽  
Special Cases ◽  
The Family ◽  
Family Of Distributions

In this work, a new family of distributions, which extends the Beta transmuted family, was obtained, called the Modified Beta Transmuted Family of distribution. This derived family has the Beta Family of Distribution and the Transmuted family of distribution as subfamilies. The Modified beta transmuted frechet, modified beta transmuted exponential, modified beta transmuted gompertz and modified beta transmuted lindley were obtained as special cases. The analytical expressions were studied for some statistical properties of the derived family of distribution which includes the moments, moments generating function and order statistics. The estimates of the parameters of the family were obtained using the maximum likelihood estimation method. Using the exponential distribution as a baseline for the family distribution, the resulting distribution (modified beta transmuted exponential distribution) was studied and its properties. The modified beta transmuted exponential distribution was applied to a real life time data to assess its flexibility in which the results shows a better fit when compared to some competitive models.

scholarly journals Bayesian and Classical Inference under Type-II Censored Samples of the Extended Inverse Gompertz Distribution with Engineering Applications

Entropy ◽  
2021 ◽  
Vol 23 (12) ◽  
pp. 1578
Author(s):  
Ahmed Elshahhat ◽  
Hassan M. Aljohani ◽  
Ahmed Z. Afify
Keyword(s):  
Real Life ◽  
Rate Function ◽  
Parameter Distribution ◽  
Model Parameters ◽  
Alpha Power ◽  
Type Ii ◽  
Failure Rate Function ◽  
Censored Samples ◽  
Inverse Gamma ◽  
Bathtub Shape

In this article, we introduce a new three-parameter distribution called the extended inverse-Gompertz (EIGo) distribution. The implementation of three parameters provides a good reconstruction for some applications. The EIGo distribution can be seen as an extension of the inverted exponential, inverse Gompertz, and generalized inverted exponential distributions. Its failure rate function has an upside-down bathtub shape. Various statistical and reliability properties of the EIGo distribution are discussed. The model parameters are estimated by the maximum-likelihood and Bayesian methods under Type-II censored samples, where the parameters are explained using gamma priors. The performance of the proposed approaches is examined using simulation results. Finally, two real-life engineering data sets are analyzed to illustrate the applicability of the EIGo distribution, showing that it provides better fits than competing inverted models such as inverse-Gompertz, inverse-Weibull, inverse-gamma, generalized inverse-Weibull, exponentiated inverted-Weibull, generalized inverted half-logistic, inverted-Kumaraswamy, inverted Nadarajah–Haghighi, and alpha-power inverse-Weibull distributions.

scholarly journals Statistical inferences for type-II hybrid censoring data from the alpha power exponential distribution

PLoS ONE ◽  
2021 ◽  
Vol 16 (1) ◽  
pp. e0244316
Author(s):  
Mukhtar M. Salah ◽  
Essam A. Ahmed ◽  
Ziyad A. Alhussain ◽  
Hanan Haj Ahmed ◽  
M. El-Morshedy ◽  
...  
Keyword(s):  
Exponential Distribution ◽  
Information Matrix ◽  
Expectation Maximization Algorithm ◽  
Location Parameter ◽  
Real Data ◽  
Estimation Methods ◽  
Invariance Property ◽  
Alpha Power ◽  
Type Ii ◽  
Hazard Functions

This paper describes a method for computing estimates for the location parameter μ > 0 and scale parameter λ > 0 with fixed shape parameter α of the alpha power exponential distribution (APED) under type-II hybrid censored (T-IIHC) samples. We compute the maximum likelihood estimations (MLEs) of (μ, λ) by applying the Newton-Raphson method (NRM) and expectation maximization algorithm (EMA). In addition, the estimate hazard functions and reliability are evaluated by applying the invariance property of MLEs. We calculate the Fisher information matrix (FIM) by applying the missing information rule, which is important in finding the asymptotic confidence interval. Finally, the different proposed estimation methods are compared in simulation studies. A simulation example and real data example are analyzed to illustrate our estimation methods.

Reliability Estimation for the Two-Parameter Exponential Family Based on Progressively Type-II Censored Data

2018 ◽  
Vol 25 (01) ◽  
pp. 1850005
Author(s):  
Wenhao Gui
Keyword(s):  
Reliability Function ◽  
Reliability Estimation ◽  
Type Ii ◽  
Prior Density ◽  
Monte Carlo Simulation Study ◽  
Censored Samples ◽  
Type Ii Censored Data ◽  
Two Parameters ◽  
Parameter Case ◽  
Two Parameter

In this paper, we deal with the problem of estimating the reliability function of the two-parameter exponential distribution. Classical Maximum likelihood and Bayes estimates for one and two parameters and the reliability function are obtained on the basis of progressively type-II censored samples. The inverted gamma conjugate prior density is assumed for the one-parameter case, whereas the joint prior density of the two-parameter case is composed of the inverted gamma and the uniform densities. A comparison between the obtained estimators is made through a Monte Carlo simulation study. A real example is used to illustrate the proposed methods.

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