Hülya Bayrak

Goodness of fit tests for Nakagami distribution based on smooth tests

ABSTRACT Nakagami distribution is one of the most common distributions used to model positive valued and right skewed data. In this study, we interest goodness of fit problem for Nakagami distribution. Thus, we propose smooth tests for Nakagami distribution based on orthonormal functions. We also compare these tests with some classical goodness of fit tests such as Cramer–von Mises, Anderson–Darling, and Kolmogorov–Smirnov tests in respect to type-I error rates and powers of tests. Simulation study indicates that smooth tests give better results than these classical tests give in respect to almost all cases considered.

Optimal Asymptotic Tests for Nakagami Distribution

Nakagami distribution is often used to model positive valued data with right skewness. The distribution includes some familiar distributions as special cases such as Rayleigh and Half-normal distributions. In real life applications, one of the simpler model may be sufficient to describe data. The aim of this paper is to adapt tests of goodness of fit of the Rayleigh distribution against Nakagami distribution. In this study likelihood ratio, and score tests are specifically obtained. These tests are then compared in terms of type I error and power of test by a Monte Carlo simulation study.

Çapraz Tasarımlarda Etkilerin Testi için Parametrik ve Parametrik Olmayan Testlerin Karşılaştırılması

Capraz tasarimlar, psikolojik denemeler, tarim, zooloji gibi bircok alanda kullanilan tasarimlardir. Bu tasarimlar daha az orneklem kullanarak daha guclu sonuclar elde etmek amaciyla kullanilirlar. Bu durum, capraz tasarimlarin onemli avantajlarindan biridir. Calismada, capraz tasarimi hakkinda ayrintili bilgi verilmistir. Capraz tasarimda etkilerin analizi icin kullanilan t testi ve Mann Whitney U testi simulasyon yoluyla deneysel I. tip hata oranlari ve guc degerleri bakimindan karsilastirilmistir. Bu amacla farkli ornek caplari, farkli korelasyon katsayilari ele alinmis ve ayrica testlerin performanslari normal ve normal olmayan dagilimlar altinda incelenmistir. Simulasyon sonuclarina gore, normal dagilim altinda t testinin guc degerleri daha yuksek iken, normal olmayan dagilimlar altinda Mann Whitney U testinin guc degerlerinin daha yuksek oldugu gozlenmistir.

Comparisons of tests of distributional assumption in Poisson regression model

ABSTRACT Count data consists of discrete non-negative integer values. Poisson regression model is one of the most popular model used to model count data. This model assumes that response variable has Poisson distribution. The purpose of this article is to assess distributional assumption of this model by using some goodness of fit tests. These tests are compared in respect to type I error and power rates of tests with different samples, parameters and sample sizes. Simulation study suggests that the most powerful tests are generally Dean–Lawless and Cameron–Trivedi score tests.