scholarly journals Tests of exponentiality against some parametric over/under-dispersed life time models

2017 ◽  
Vol 21 (2) ◽  
pp. 207-223
Author(s):  
Rajibul Mian ◽  
Sudhir Paul
Keyword(s):  
Exponential Distribution ◽  
Goodness Of Fit ◽  
Score Test ◽  
Life Time ◽  
Exponential Model ◽  
Maximum Likelihood Estimates ◽  
Test Statistics ◽  
Overall Performance ◽  
Likelihood Ratio Statistics ◽  
Family Of Distributions

We develop tests of goodness of fit of the exponential model against some over/under dispersion family of distributions. In particular, we develop 3 score test statistics and 3 likelihood ratio statistics. These are (S1, L1), (S2, L2), and (S3, L3) based on a general over-dispersed family of distributions, two specic over/under dispersed exponential models, namely, the gamma and the Weibull distributions, respectively. A simulation study shows that the statistics S3 and L3 have best overall performance, in terms of both, level and power. However, the statistic L3 can be liberal in some instances and it needs the maximum likelihood estimates of the parameters of the Weibull distribution as opposed to the statistic S3 which is very simple to use. So, our recommendation is to use the statistic S3 to test the fit of an exponential distribution over any over/under-dispersed exponential distribution.

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 The Logarithmic Burr-Hatke Exponential Distribution for Modeling Reliability and Medical Data

2018 ◽  
Vol 7 (5) ◽  
pp. 73
Author(s):  
T. H. M. Abouelmagd
Keyword(s):  
Exponential Distribution ◽  
Exponential Model ◽  
Likelihood Method ◽  
Model Parameters ◽  
Suitable Model ◽  
Monte Carlo Simulation Study ◽  
New Model ◽  
Weibull Models ◽  
Modified Weibull ◽  
Family Of Distributions

In this work, we introduced a new one-parameter exponential distribution. Some of its structural properties are derived% \textbf{.} The maximum likelihood method is used to estimate the model parameters by means of numerical Monte Carlo simulation study. The justification for the practicality of the new lifetime model is based on the wider use of the exponential model. The new model can be viewed as a mixtureof the exponentiated exponential distribution. It can also be considered as a suitable model for fitting right skewed data.\textbf{\ }We prove empirically the importance and flexibility of the new model in modelingcancer patients data, the new model provides adequate fits as compared to other related models with small values for $W^{\ast }$\ \ and $A^{\ast }$. The new model is much better than the Modified beta-Weibull, Weibull, exponentiated transmuted generalized Rayleig, the transmuted modified-Weibull, and transmuted additive Weibull models in modeling cancer patients data. We are also motivated to introduce this new model because it has only one parameter and we can generate some new families based on it such as the the odd Burr-Hatke exponential-G family of distributions, the logarithmic\textbf{\ }Burr-Hatke exponential-G family of distributions and the generalized\textbf{\ }Burr-Hatke exponential-G family of distributions, among others.

scholarly journals A New Poisson Inverted Exponential Distribution: Model, Properties and Application

2020 ◽  
pp. 136-146
Author(s):  
Govinda Prasad Dhungana
Keyword(s):  
Exponential Distribution ◽  
Goodness Of Fit ◽  
Residual Life ◽  
Life Time ◽  
Real Data ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Distribution Model ◽  
Time Data ◽  
Unknown Parameters

A new Poisson Inverted Exponential distribution is developed from the Poisson family of distribution, which has two parameters. The characteristic of the intended model is unimodal, positive skewed and platykurtic, while the characteristic of the hazard function is the inverted bathtub and the decreasing order. Explicit expression of quantile function, moments (including incomplete and conditional moments), moment generating function, residual life function, R`enyi and q-entropies, probability weighted moment and order statistics of the intended model. The value of unknown parameters is estimated by the maximum likelihood estimate with the confidence interval. Similarly, purposed model compared with well-known other five distributions through different criteria like as goodness of fit, P-P plot, Q-Q plots and K-S test. Likewise, we fitted the PDF and CDF of purposed model with other models, it is clear that intended model is great flexibility and satisfactory fit than those models. Therefore purposed model is more useful in real data and life time data analysis and modelling.

A Bivariate Exponential Model with Covariates in Competing Risk Data

1996 ◽  
Vol 46 (3-4) ◽  
pp. 197-210 ◽  
Author(s):  
Cicilia Yuko Wada ◽  
Pranab Kumar Sen ◽  
Silvia Emiko Shimakura
Keyword(s):  
Exponential Distribution ◽  
Risk Model ◽  
Score Test ◽  
Exponential Model ◽  
Competing Risk ◽  
Test Statistic ◽  
Bivariate Exponential Distribution ◽  
Competing Risk Model ◽  
Bivariate Exponential ◽  
Causes Of Failure

Sarkar's bivariate exponential distribution is incorporated in a competing risk model with two causes of failure. In view of the nonidentifiability of the parameters of this distribution under competing risk, reparameterization is advocated and covariates are related to the reparameterized parameters through logistic and log­linear models. The restricted alternative hypothe,is is considered for the comparison of the survival distributions of the two causes of failure, the test statistic based on Roy's union­intersection principle is used and compared with the score test statistic. An application is also considered,

scholarly journals Goodness-of-Fit Tests for Bivariate Time Series of Counts

Econometrics ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 10
Author(s):  
Šárka Hudecová ◽  
Marie Hušková ◽  
Simos G. Meintanis
Keyword(s):  
Goodness Of Fit ◽  
Probability Generating Function ◽  
Parametric Bootstrap ◽  
Real Data ◽  
Data Sets ◽  
Test Statistics ◽  
Finite Sample ◽  
Generalized Poisson ◽  
Goodness Of Fit Tests ◽  
Monte Carlo Experiments

This article considers goodness-of-fit tests for bivariate INAR and bivariate Poisson autoregression models. The test statistics are based on an L2-type distance between two estimators of the probability generating function of the observations: one being entirely nonparametric and the second one being semiparametric computed under the corresponding null hypothesis. The asymptotic distribution of the proposed tests statistics both under the null hypotheses as well as under alternatives is derived and consistency is proved. The case of testing bivariate generalized Poisson autoregression and extension of the methods to dimension higher than two are also discussed. The finite-sample performance of a parametric bootstrap version of the tests is illustrated via a series of Monte Carlo experiments. The article concludes with applications on real data sets and discussion.

scholarly journals Survival and Reliability Analysis with an Epsilon-Positive Family of Distributions with Applications

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 908
Author(s):  
Perla Celis ◽  
Rolando de la Cruz ◽  
Claudio Fuentes ◽  
Héctor W. Gómez
Keyword(s):  
Survival Data ◽  
Maximum Likelihood Estimates ◽  
New Class ◽  
New Family ◽  
Gamma Distributions ◽  
Special Cases ◽  
Log Normal ◽  
Positive Support ◽  
Positive Distributions ◽  
Family Of Distributions

We introduce a new class of distributions called the epsilon–positive family, which can be viewed as generalization of the distributions with positive support. The construction of the epsilon–positive family is motivated by the ideas behind the generation of skew distributions using symmetric kernels. This new class of distributions has as special cases the exponential, Weibull, log–normal, log–logistic and gamma distributions, and it provides an alternative for analyzing reliability and survival data. An interesting feature of the epsilon–positive family is that it can viewed as a finite scale mixture of positive distributions, facilitating the derivation and implementation of EM–type algorithms to obtain maximum likelihood estimates (MLE) with (un)censored data. We illustrate the flexibility of this family to analyze censored and uncensored data using two real examples. One of them was previously discussed in the literature; the second one consists of a new application to model recidivism data of a group of inmates released from the Chilean prisons during 2007. The results show that this new family of distributions has a better performance fitting the data than some common alternatives such as the exponential distribution.

scholarly journals The Flexible Burr X-G Family: Properties, Inference, and Applications in Engineering Science

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 474
Author(s):  
Abdulhakim A. Al-Babtain ◽  
Ibrahim Elbatal ◽  
Hazem Al-Mofleh ◽  
Ahmed M. Gemeay ◽  
Ahmed Z. Afify ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Exponential Distribution ◽  
Real Data ◽  
Exponential Model ◽  
Statistical Properties ◽  
Engineering Science ◽  
Data Sets ◽  
Engineering Sciences ◽  
General Statistical ◽  
Anderson Darling

In this paper, we introduce a new flexible generator of continuous distributions called the transmuted Burr X-G (TBX-G) family to extend and increase the flexibility of the Burr X generator. The general statistical properties of the TBX-G family are calculated. One special sub-model, TBX-exponential distribution, is studied in detail. We discuss eight estimation approaches to estimating the TBX-exponential parameters, and numerical simulations are conducted to compare the suggested approaches based on partial and overall ranks. Based on our study, the Anderson–Darling estimators are recommended to estimate the TBX-exponential parameters. Using two skewed real data sets from the engineering sciences, we illustrate the importance and flexibility of the TBX-exponential model compared with other existing competing distributions.

scholarly journals An Universal, Simple, Circular Statistics-Based Estimator of α for Symmetric Stable Family

2019 ◽  
Vol 12 (4) ◽  
pp. 171
Author(s):  
Ashis SenGupta ◽  
Moumita Roy
Keyword(s):  
Entire Range ◽  
Goodness Of Fit ◽  
Stable Distribution ◽  
Real Life ◽  
Circular Statistics ◽  
Directional Statistics ◽  
Symmetric Stable Distribution ◽  
Stable Family ◽  
Family Of Distributions ◽  
Better Than

The aim of this article is to obtain a simple and efficient estimator of the index parameter of symmetric stable distribution that holds universally, i.e., over the entire range of the parameter. We appeal to directional statistics on the classical result on wrapping of a distribution in obtaining the wrapped stable family of distributions. The performance of the estimator obtained is better than the existing estimators in the literature in terms of both consistency and efficiency. The estimator is applied to model some real life financial datasets. A mixture of normal and Cauchy distributions is compared with the stable family of distributions when the estimate of the parameter α lies between 1 and 2. A similar approach can be adopted when α (or its estimate) belongs to (0.5,1). In this case, one may compare with a mixture of Laplace and Cauchy distributions. A new measure of goodness of fit is proposed for the above family of distributions.

Explosion Recurrence Modelling

2004 ◽  
Author(s):  
Sirous F. Yasseri ◽  
Jake Prager
Keyword(s):  
Risk Assessment ◽  
Goodness Of Fit ◽  
Residential Buildings ◽  
Limit State ◽  
Life Time ◽  
Assessment Method ◽  
The North ◽  
Offshore Installations ◽  
Risk Assessment Method ◽  
Explosion Load

This paper describes a recurrence law for explosions. The proposed recurrence law fits quite well to the historic explosion data in residential buildings as well as to the data on offshore installations in the North Sea. Generally quantified explosion risk assessment is performed for offshore installations, since it is believed historic data does not correspond to a specific installation and it may not be appropriate for use in performance based explosion engineering, which may in itself require realistic load description of explosion recurrence. The goodness-of-fit of the model for explosion occurrence data obtained using the quantified risk assessment method is also discussed. The paper then introduces the concept of performance-based design, which is an attempt to design structures with predictable performance under explosion loading. Performance objectives such as life safety, collapse prevention, or immediate resumption of operation are used to define the state of an installation following a design explosion. The recurrence law is then used to associate a level of explosion load to each limit state using a desirable level of probability of exceedance during the installations life time.

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