Yazar "Erol, Hamza" seçeneğine göre listele

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    The mixed weibullnegative binomial distribution
    (Selcuk University Research Center of Applied Mathematics, 2011) Korkmaz, Mustafa Çağatay; Kuş, Coşkun; Erol, Hamza
    In this paper, we introduce the Weibull Negative Binomial (WNB) with four parameters distribution which is obtained by compounding Weibull and Negative Binomial distributions, where compounding procedure follows same way that was previously carried out by Adamidis and Loukas (1998) and Kus (2007). This new distribution is a genaral case Exponential-geometric (EG) and Weibull-geometric distributions (WG), which was introduced recently by Adamidis and Loukas (1998) and Barreto-Souza et. all. (2010) respectively. The WNB distribution has increasing, decreasing, upside down bathtub hazard function. We obtain several properties of the WNB distributions such as moments, order statistics, estimation by maximum likelihood and inference for large sample. Furthermore, EM algorithm is also used to determine the maximum likelihood estimates of parameters and we discuss Renyi and Shannon entropy. Applications to real data sets are given to show the exibility and potentiality of the proposed distribution.
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    Mixture distribution model approximation to system reliability
    (Selcuk University Research Center of Applied Mathematics, 2011) Türkan, Ayça Hatice; Erol, Hamza
    In this study, mixture reliability functions, mixture probability density functions and mixture hazard functions were established for reliability block diagrams of series, parallel and complex systems. Mixture reliability function, mixture probability density function and mixture hazard function, established for systems studied, were proposed as an approximation to reliability function, probability density function and hazard function respectively. It was shown that system reliability functions, system probability density functions and system hazard functions can be expressed in terms of component reliability functions, component probability density functions and component hazard functions respectively. By the mixture distribution model approximation to system reliability: function representations were simplified, function calculations were decreased and information extracted from the system and its components were increased for reliability block diagrams of series, parallel and complex systems.
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    Mixture Model Approach to the Analysis of Heterogeneous Survival Data
    (Isoss Publ, 2012) Erisoğlu, Ülkü; Erisoğlu, Murat; Erol, Hamza
    In this paper, we examine mixture models to model heterogeneous survival data. Mixture of Gamma distributions, mixture of Lognormal distributions and mixture of Weibull distributions were tested for the best fit to the real survival datasets. Various properties of the proposed mixture models were discussed. Maximum likelihood estimations of the parameters of mixture models were obtained by the EM algorithm. The mixture models were successfully applied for modeling two real heterogeneous survival datasets.
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    A note on non-identifibiality problem of finite mixture distribution models in model-based classification
    (Selcuk University Research Center of Applied Mathematics, 2004) Erol, Hamza
    The probability density functions (pdfs) of the mixture distribution models (mdms) for two different populations can be compared by using a distance function (metric) between them in model-based classification applications. The result of the comparison may not be true if the component densities of the mdms are permutation functions. Thus, non-identifibiality problem of finite mixture distribution models. In other words, the order of the component densities of the mdms should be taken into account. If the component densities of the mdms are permutation functions then the pdfs of the mdms for two different population looks like similar but in fact they are completely different. Such a case may cause wrong inference in the applications in which the mdms used, for example in classification applications. The componentwise distance function is proposed for the comparison of the pdfs of the mdms for two different populations if the component densities are permutation functions. The condition under which the value of the distance function between the pdfs of the mdms for two different populations is equal to the value of the componentwise distance function between the pdfs of the mdms for two different populations is given.
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    On total number of candidate component cluster centers and total number of candidate mixture models in model based clustering
    (Selcuk University Research Center of Applied Mathematics, 2007) Servi, Tayfun; Erol, Hamza
    Determining the number of component clusters for a multivariate normal mixture model is the most important problem in model based clustering and determining the number of candidate mixture models is the most interesting problem in multivariate normal mixture model based clustering using model selection criteria. In this study; first, the concept of the total number of candidate component cluster centers is introduced and an interval is constructed by using the number of partitions in each variable in multivariate data. Second, an equation is given for the total number of candidate mixture models in multivariate normal mixture model based clustering. The number of candidate mixture models is defined as the sum of the number of possible mixture models with different number of component clusters.