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APT-Pareto Distribution and its Properties
(2019) Kınacı, İsmail; Kuş, Coşkun; Karakaya, Kadir; Akdoğan, Yunus
Recently, the APT-family has been introduced as a new family of distributions. A special case of this family with exponential distribution is examined in details. In this paper, Pareto is considered as a baseline distribution in APT-family. Several properties of the APT-Pareto distribution such as the moments, hazard rate and survival functions are derived. The maximum likelihood and least square methods are discussed. Simulation study is also performed to get the bias and mean square errors of estimates. A numerical example is given to illustrate the capability of APT-Pareto distribution for modelling real data.
Binomial-discrete Lindley distribution
(ANKARA UNIV, FAC SCI, 2019) Kuş, Coşkun; Akdoğan, Yunus; Asgharzadeh, Akbar; Kınacı, İsmail; Karakaya, Kadir
In this paper, a new discrete distribution called Binomial-Discrete Lindley (BDL) distribution is proposed by compounding the binomial and discrete Lindley distributions. Some properties of the distribution are discussed including the moment generating function, moments and hazard rate function. The estimation of distribution parameter is studied by methods of moments, proportions and maximum likelihood. A simulation study is performed to compare the performance of the different estimates in terms of bias and mean square errors. Automobile claim data applications are also presented to see that the new distribution is useful in modelling data.
Discriminating between the Lognormal and Weibull Distributions under Progressive Censoring
(2019) Kuş, Coşkun; Pekgör, Ahmet; Kınacı, İsmail
In this paper, the ratio of maximized likelihood and Minimized Kullback-Leibler Divergencemethods are discussed for discrimination between log-normal and Weibull distributions. The progressive Type-II right censored sample is considered in the study. The probability of correct selections is simulated andcompared to investigate the performance of the procedures for different censoring schemes and parametersettings.
Estimation of parameters of the loglogistic distribution based on progressive censoring using the EM algorithm
(2006) Kuş, Coşkun; Kaya, Mehmet Fedai
Although the maximum likelihood estimation method based on pro- gressively censored data has been studied extensively, traditionally the Newton-Raphson method has been used to obtain the estimates (Ng et al., 2002). As pointed out by Little and Rubin in 1983, the EM algorithm will converge reliably but rather slowly (as compared to the Newton-Raphson method) when the amount of information in the missing data is relatively large. Therefore, in this study, maximum likelihood estimates for the parameters of the Loglogistic distribution are obtained using the EM algorithm based on a progressive Type-II right censored sample. An illustrative example is also given.
Geometric-zero truncated poisson distribution: properties and applications
(GAZI UNIV, 2019) Akdoğan, Yunus; Kuş, Coşkun; Bidram, Hamid; Kınacı, İsmail
In this paper, a new discrete distribution is introduced by compounding the geometric distribution with a zero truncated Poisson distribution, named geometric-zero truncated Poisson (GZTP) distribution. Some basic properties of the new distribution, such as the hazard rate function, moments, mode, median, etc., are studied. We show mathematically and numerically that the hazard rate function is increasing. The model parameters are estimated by the moment, least squared error and maximum likelihood methods. A simulation study is performed to compare the performance of the different estimators in terms of bias and mean squared error. An application of the new model is also illustrated using the three real data sets.
İki Örneklem Problemi İçin Yeni Bir Test İstatistiği ve Gücünün Diğer Testlerle Karşılaştırılması
(Selçuk Üniversitesi Fen-Edebiyat Fakültesi, 2003) Kaya, Mehmet Fedai; Kuş, Coşkun
Bu çalışmada, sürekli dağılımlar ailesi için dağılımdan bağımsız yeni bir istatistik önerilmiş, bu istatistiğin kesin dağılımı, için bilgisayar programı kullanılarak uygun durumların sayılmasıyla, ve için amprik dağılımı Monte Carlo simulasyon yöntemiyle elde edilmiştir. Testin gücü Monte Carlo simulasyon yöntemi kullanılarak Kolmogorov-Smirnov, Mann- Whitney Wilcoxon ve İşaret testlerinin gücü ile karşılaştırılmıştır.
İlerleyen Tür Sansürlü Verilere Dayalı Aralık Tahmini
(Selçuk Üniversitesi Fen Fakültesi Fen Dergisi, 2016) Kuş, Coşkun; Çökek, Nagihan; Kınacı, İsmail; Akdoğan, Yunus; Karakaya, Kadir
Bu çalışmada, literatürde olan bir pivot kullanılarak Weibull, Burr XII ve Gompertz dağılımı için güven aralıkları oluşturulmuştur. İstatistiksel sonuç çıkarımı ilerleyen sansürleme altında tartışılmıştır. Pivot elemanın dağılımı literatürde verilen tablolara göre farklı sansür şemaları için daha da genişletilmiştir. Tam örneklem durumunda, regresyon modelleri pivot elemanının sınır değerlerini elde etmek için tahmin edilmiştir. Ayrıca sayısal bir örnek verilmiştir.
Interval estimation for the two-parameter pareto distribution based on record values
(Selcuk University Research Center of Applied Mathematics, 2011) Asgharzadeh, A.; Abdi, M.; Kuş, Coşkun
This paper considers the interval estimation problem for the Pareto distribution based on record statistics. We present some exact confidence intervals and exact joint confidence regions for the parameters of Pareto distribution based on record statistics. One of the applications of the joint confidence regions of the parameters is to find confidence bounds for the functions of the parameters. In addition, the predictive interval of the future record based on the observed record values is also proposed. A Monte Carlo simulation is conducted to compare the proposed joint confidence regions. Finally, two numerical examples are given also to illustrate the methods proposed in this paper.
Kesikli Chen Dağılımı için Bayes Tahmini
(Selçuk Üniversitesi Fen Fakültesi Fen Dergisi, 2016) Kınacı, İsmail; Karakaya, Kadir; Akdoğan, Yunus; Kuş, Coşkun
Bu çalışmada, Kesikli Chen dağılımı için bayes tahmini incelenmiştir. Bayes tahmin edicilerini elde etmek zor olduğundan Bayes tahminlerinin yaklaşık değerleri Tierney-Kadane yaklaşımı kullanılarak elde edilmiştir. Tahmin edicilerin performansını gözlemlemek için simülasyon çalışmaları yapılmıştır. Ayrıca sayısal bir örnek verilmiştir.
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.
A new family of distributions
(HACETTEPE UNIV, FAC SCI, 2017) Karakaya, Kadir; Kınacı, İsmail; Kuş, Coşkun; Akdoğan, Yunus
In this study, a new family of distributions is introduced which is called alpha log-transformation family. We consider a special case of this family with exponential distribution in details. Several properties of the proposed distribution including the raw moments, moment generating function, quantile function and hazard rate function are obtained. Statistical inference is discussed based on complete and progressive censored samples. Simulation study is also performed to observe the performance of the estimates and approximate confidence intervals. A real data is given to illustrate the capability of ALT- Exponential distribution for modelling real data.
ON THE NUMBER OF l--OVERLAPPING SUCCESS RUNS OF LENGTH k UNDER q-- SEQUENCE OFBINARY TRIALS
(2016) Kinaci, Ismail; Kuş, Coşkun; Karakaya, Kadir; Akdoğan, Yunus
Let X1,X2,...,X.. be {0,1}-valued Bernoulli trials with geometrically varying success probability. The probability mass function, first and second moments of the number of l-overlapping success runs of length k: in X1,X2,...,X,, are obtained. The new distribution generalizes, Type and Type II q-binomial distributions which were recently studied in the literature.
Optimal progressive group censoring scheme under cost considerations for pareto distribution
(TAYLOR & FRANCIS LTD, 2013) Kuş, Coşkun; Akdoğan, Yunus; Wu, Shuo-Jye
In this article, optimal design under the restriction of pre-determined budget of experiment is developed for the Pareto distribution when the life test is progressively group censored. We use the maximum-likelihood method to obtain the point estimator of the Pareto parameter. We propose two approaches to decide the number of test units, the number of inspections, and the length of inspection interval under limited budget such that the asymptotic variance of estimator of Pareto parameter is minimum. A numerical example is given to illustrate the proposed method. Some sensitivity analysis is also studied.
Optimal progressive group-censoring plans for Chen distribution under cost constraint
(ISOSS PUBLICATIONS, 2015) Akdoğan, Yunus; Kuş, Coşkun; Wu, Shuo-jye
In this paper, the optimal design of a progressively group-censored life test with the restriction of experimental budget is developed for the Chen distribution is considered. The maximum likelihood estimates, approximate confidence intervals for the parameters based on progressively group-censored sample are obtained. Wu et al.’s (2008a) approach is used to determine the number of test units, the number of inspections and the length of inspection interval of a life test under a pre-determined budget of experiment such that the determinant of the asymptotic variances-covariance matrix of estimators of parameters is minimum. A numerical example is presented and the sensitivity analysis is also studied. © 2015 Pakistan Journal of Statistics.
Pareto I Dağılımının İlk Bozulma Sansürlü Örnekleme Planına Dayalı Parametrelerinin Tahmini ve Beklenen Test Süresi
(Selçuk Üniversitesi Fen-Edebiyat Fakültesi, 2004) Kuş, Coşkun; Kaya, Mehmet Fedai
Bu çalışmada, ilk bozulma sansürlü örnekleme planı ele alınmıştır. Pareto I dağılımının parametrelerinin yeni tahmin edicileri Menon’un [8] yöntemine benzer olarak elde edilmiş ve özellikleri Monte Carlo simulasyon çalışması yapılarak incelenmiştir. Parametreler için güven aralıkları ve güven bölgeleri elde edilmiştir. Ayrıca ilk bozulma sansürlü örnekleme planına dayalı beklenen test süresi hesaplanmış ve tam örnekleme planın ki ile karşılaştırılmıştır.
Planning life tests for Burr XII distributed products under progressive group-censoring with cost considerations
(2012) Akdoğan, Yunus; Kuş, Coşkun; Wu, Shou-jye
In this paper, a progressive type I group-censoring life test for Burr XII distribution is considered. We use the maximum likelihood method to obtain the point estimators of the Burr XII parameters. The approximate confidence intervals for the parameters of Burr XII distribution are also obtained. We use modified algorithm proposed by Kus et al. [20] to decide the number of test units, number of inspections, and length of inspection interval under a restricted budget of experiment such that the determinant of the asymptotic variances-covariance of estimators of parameters is minimum. A numerical example is presented to illustrate the proposed approach. The sensitivity analysis is also investigated.
Uniform-Geometric distribution
(TAYLOR & FRANCIS LTD, 2016) Akdoğan, Yunus; Kuş, Coşkun; Asgharzadeh, Akbar; Kiınacı, İsmail; Sharafi, Fatemeh
In this paper, a new discrete distribution called Uniform-Geometric distribution is proposed. Several distributional properties including survival function, moments, skewness, kurtosis, entropy and hazard rate function are discussed. Estimation of distribution parameter is studied by methods of moments, proportions and maximum likelihood. A simulation study is performed to compare the performance of the different estimates in terms of bias and mean square error. Two real data applications are also presented to see that new distribution is useful in modelling data.

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