Oransal lindley fréchet dağılımının bazı teorik ve hesaplamalı yönleri

In this article, we study an extension of the Fréchet model by using the the odd Lindley-G family of distributions, which was introduced by [17]. Its some statistical properties such as quantile function, density shapes, moments, generating functions and order statistics are obtained. We estimate its parameters by maximum likelihood method. The Monte Carlo simulation is used for assessing the performance of the maximum likelihood method. The usefulness of the odd Lindley Fréchet model is illustrated by means of three real data sets.Bu çalışmada, Fréchet modelinin genişletilmiş bir versiyonu [17] tarafından önerilen oransal Lindley dağılım ailesi kullanılarak çalışılmıştır. Bu modele ait kuantil fonksiyonu, yoğunluk biçimi, momentler, üreten fonksiyon ve sıra istatistikleri gibi istatistiksel özellikleri elde edilmiştir. Model parametrelerinin en çok olabilirlik tahminleri elde edildi. En çok olabilirlik parametre tahminleri için bir simülasyon çalışılması verilmiştir. Önerilen modelin gerçek veri seti üzerindeki uygunluğu için üç veri analizi yapılmıştır

Double Truncated Transmuted Fréchet Distribution: Properties and Applications

In this paper, we modify the Mahmoud and Mandouh (2013) model by adopting double truncation technique. It is referred to as Double Truncated Transmuted Fréchet (DTTF) distribution. Diverse probabilistic and reliability measures are developed and discussed. The MLEs of parameters are derived and a simulation study is also made. The DTTF distribution is modeled by two real-time datasets and supportive rationalized results provide the evidence that DTTF distribution is a reasonably better fit model than its competing models. Keywords: Fréchet Distribution, Double Truncation, Hazard Function, Moments, MLE, Quadratic Rank Transmutation Map (QRTM), Rényi entropy, Order Statistics. DOI: 10.7176/MTM/9-3-02 Publication date: March 31st 201

Classes of Ordinary Differential Equations Obtained for the Probability Functions of Frĕchet Distribution

In this paper, the differential calculus was used to obtain some classes of ordinary differential equations (ODE) for the probability density function, quantile function, survival function, inverse survival function, hazard function and reversed hazard function of the Frĕchet distribution. The stated necessary conditions required for the existence of the ODEs are consistent with the various parameters that defined the distribution. Solutions of these ODEs by using numerous available methods are a new ways of understanding the nature of the probability functions that characterize the distribution. The method can be extended to other probability distributions and can serve an alternative to approximation

Classes of Ordinary Differential Equations Obtained for the Probability Functions of Frĕchet Distribution

In this paper, the differential calculus was used to obtain some classes of ordinary differential equations (ODE) for the probability density function, quantile function, survival function, inverse survival function, hazard function and reversed hazard function of the Frĕchet distribution. The stated necessary conditions required for the existence of the ODEs are consistent with the various parameters that defined the distribution. Solutions of these ODEs by using numerous available methods are a new ways of understanding the nature of the probability functions that characterize the distribution. The method can be extended to other probability distributions and can serve an alternative to approximation

Generalising Exponential Distributions Using an Extended Marshall-Olkin Procedure

This paper presents a three-parameter family of distributions which includes the common exponential and the Marshall–Olkin exponential as special cases. This distribution exhibits a monotone failure rate function, which makes it appealing for practitioners interested in reliability, and means it can be included in the catalogue of appropriate non-symmetric distributions to model these issues, such as the gamma and Weibull three-parameter families. Given the lack of symmetry of this kind of distribution, various statistical and reliability properties of this model are examined. Numerical examples based on real data reflect the suitable behaviour of this distribution for modelling purposes