Testing the number of components of the mixture of two inverse Weibull distributions

Ismail, Moshira A.; Al-Moisheer, A. S.

doi:10.1080/00207160701690425

Cited by 5 publications

(6 citation statements)

References 16 publications

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“…Jiang et al [17] discuss the aging property of the unimodal failure rate models including the IW distribution. Sultan et al [18,19] discuss the properties of a mixture of two IW distributions, prove the distribution is identifiable, and investigate testing for the number of components. Gusmão et al [20] propose and discuss the properties of a generalized IW distribution.…”

Section: Preliminarymentioning

confidence: 99%

“…i = 1, … , n, where 1 and 2 denote vectors of coefficients, so that for each group of individuals, represented by x 1i and x 2i , we have possibly different non-default fraction and scale parameters. From (19), we can write the likelihood function of = ( 1 , 2 , ) ⊤ under non-informative censoring as where  = (t, , x 1 , x 2 ), t = (t 1 , … , t n ) ⊤ and = ( 1 , … , n ) ⊤ denote the n-dimensional vectors of times-to-default and censoring, respectively, x j = (x j1 , … , x jn ) ⊤ , j = 1, 2, were defined earlier, and f GIWnd (⋅; ) and S GIWnd (⋅; ) are the improper PDF and surviving functions given in (5)- (10). From the likelihood function in (20), the maximum likelihood estimation of the parameter is carried out.…”

Section: Estimationmentioning

confidence: 99%

“…Sultan et al . discuss the properties of a mixture of two IW distributions, prove the distribution is identifiable, and investigate testing for the number of components. Gusmão et al .…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A non‐default rate regression model for credit scoring

Barriga

Cancho

Louzada

2015

Appl Stoch Models Bus & Ind

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In this paper, we propose a new non‐default rate survival model. Our approach enables different underlying activation mechanisms which lead to the event of interest. The number of competing causes, which may be responsible for the occurrence of the event of interest, is assumed to follow a geometric distribution, while the time to event is assumed to follow an inverse Weibull distribution. An advantage of our approach is to accommodate all activation mechanisms based on order statistics. We explore the use of maximum likelihood estimation procedure. Simulation studies are performed and experimental results are illustrated based on a real Brazilian bank personal loan portfolio data. Copyright © 2015 John Wiley & Sons, Ltd.

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Section: Preliminarymentioning

confidence: 99%

Section: Estimationmentioning

confidence: 99%

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A non‐default rate regression model for credit scoring

Barriga

Cancho

Louzada

2015

Appl Stoch Models Bus & Ind

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“…An alternative approach for testing the number of components g in mixture models is to obtain an empirical distribution of the test statistic via Monte Carlo simulation, when the usual asymptotic null distribution of chisquared distribution of the test statistic is not applicable. [36] used this approach to simulate the LRT statistic for testing homogeneity in a mixture of two inverse Weibull distributions. Recently, [18] constructed the empirical distribution of the EM test statistic to compute the size and power for testing homogeneity in the mixture of BS distributions.…”

Section: Introductionmentioning

confidence: 99%

Testing the Number of Components in a Birnbaum-Saunders Mixture Model under a Random Censoring Scheme

EL-Sharkawy

Ismail

2021

Stat., optim. inf. comput.

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This paper deals with testing the number of components in a Birnbaum-Saunders mixture model under randomly right censored data. We focus on two methods, one based on the modified likelihood ratio test and the other based on the shortcut of bootstrap test. Based on extensive Monte Carlo simulation studies, we evaluate and compare the performance of the proposed tests through their size and power. A power analysis provides guidance for researchers to examine the factors that affect the power of the proposed tests used in detecting the correct number of components in a Birnbaum-Saunders mixture model. Finally an example of aircraft Windshield data is used to illustrate the testing procedure.

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“…The inverse Weibull distribution has been fitted for some pieces of data from reliability engineering and biomedical studies; see Drapella [13]. Recently, Sultan et al [14,15] have discussed some properties of a mixture of two inverse Weibull distributions and the hypotheses testing problem regarding the number of components.…”

Section: Introductionmentioning

confidence: 99%

Mixture of Inverse Weibull and Lognormal Distributions: Properties, Estimation, and Illustration

Al-Moisheer

2015

Mathematical Problems in Engineering

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We discuss the two-component mixture of the inverse Weibull and lognormal distributions (MIWLND) as a lifetime model. First, we discuss the properties of the proposed model including the reliability and hazard functions. Next, we discuss the estimation of model parameters by using the maximum likelihood method (MLEs). We also derive expressions for the elements of the Fisher information matrix. Next, we demonstrate the usefulness of the proposed model by fitting it to a real data set. Finally, we draw some concluding remarks.

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Testing the number of components of the mixture of two inverse Weibull distributions

Cited by 5 publications

References 16 publications

A non‐default rate regression model for credit scoring

A non‐default rate regression model for credit scoring

Testing the Number of Components in a Birnbaum-Saunders Mixture Model under a Random Censoring Scheme

Mixture of Inverse Weibull and Lognormal Distributions: Properties, Estimation, and Illustration

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