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On characterizing the gamma and the beta $q$-distributions
Imen Boutouria,Imed Bouzida,Afif Masmoudi 대한수학회 2018 대한수학회보 Vol.55 No.5
In this paper, our central focus is upon gamma and beta $q$-distributions from a probabilistic viewpoint. The gamma and the beta $q$-distributions are characterized by investing the nature of the joint $q$-probability density function through the $q$-independence property and the $q$-Laplace transform.
ON CHARACTERIZING THE GAMMA AND THE BETA q-DISTRIBUTIONS
Boutouria, Imen,Bouzida, Imed,Masmoudi, Afif Korean Mathematical Society 2018 대한수학회보 Vol.55 No.5
In this paper, our central focus is upon gamma and beta q-distributions from a probabilistic viewpoint. The gamma and the beta q-distributions are characterized by investing the nature of the joint q-probability density function through the q-independence property and the q-Laplace transform.
On the existence of the Tweedie power parameter implicit estimator
Abdelaziz Ghribi,Aymen Hassin,Afif Masmoudi 대한수학회 2022 대한수학회보 Vol.59 No.4
A special class of exponential dispersion models is the class of Tweedie distributions. This class is very significant in statistical modeling as it includes a number of familiar distributions such as Gaussian, Gamma and compound Poisson. A Tweedie distribution has a power parameter $p$, a mean $m$ and a dispersion parameter $\phi$. The value of the power parameter lies in identifying the corresponding distribution of the Tweedie family. The basic objective of this research work resides in investigating the existence of the implicit estimator of the power parameter of the Tweedie distribution. A necessary and sufficient condition on the mean parameter $m$, suggesting that the implicit estimator of the power parameter $p$ exists, was established and we provided some asymptotic properties of this estimator.