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Articles 1 - 9 of 9
Full-Text Articles in Physical Sciences and Mathematics
Type I General Exponential Class Of Distributions, Gholamhossein G. Hamedani, Haitham M. Yousof, Mahdi Rasekhi, Morad Alizadeh, Seyed Morteza Najibi
Type I General Exponential Class Of Distributions, Gholamhossein G. Hamedani, Haitham M. Yousof, Mahdi Rasekhi, Morad Alizadeh, Seyed Morteza Najibi
Mathematics, Statistics and Computer Science Faculty Research and Publications
We introduce a new family of continuous distributions and study the mathematical properties of the new family. Some useful characterizations based on the ratio of two truncated moments and hazard function are also presented. We estimate the model parameters by the maximum likelihood method and assess its performance based on biases and mean squared errors in a simulation study framework.
Some Extended Classes Of Distributions: Characterizations And Properties, Gholamhossein G. Hamedani, Gauss M. Cordeiro, M. C.S. Lima, A. D.C. Nascimento
Some Extended Classes Of Distributions: Characterizations And Properties, Gholamhossein G. Hamedani, Gauss M. Cordeiro, M. C.S. Lima, A. D.C. Nascimento
Mathematics, Statistics and Computer Science Faculty Research and Publications
Based on a simple relationship between two truncated moments and certain functions of the th order statistic, we characterize some extended classes of distributions recently proposed in the statistical literature, videlicet Beta-G, Gamma-G, Kumaraswamy-G and McDonald-G. Several properties of these extended classes and some special cases are discussed. We compare these classes in terms of goodness-of-fit criteria using some baseline distributions by means of two real data sets.
New Classes Of Univariate Continuous Exponential Power Series Distributions, M. Ahsanullah, Gholamhossein G. Hamedani, M. Shakil, B.M. Golam Kibria, F. George
New Classes Of Univariate Continuous Exponential Power Series Distributions, M. Ahsanullah, Gholamhossein G. Hamedani, M. Shakil, B.M. Golam Kibria, F. George
Mathematics, Statistics and Computer Science Faculty Research and Publications
Recently, many researchers have developed various classes of continuous probability distributions which can be generated via the generalized Pearson differential equation and other techniques. In this paper, motivated by the importance of the power series in probability theory and its applications, we derive some new classes of univariate exponential power series distributions for a realvalued continuous random variable, which we call exponential power series distributions. Various mathematical properties of the proposed classes of distributions are discussed. Based on these distributional properties, we have established some characterizations of these distributions as well. It is hoped that the findings of the paper …
The Kumaraswamy Marshal-Olkin Family Of Distributions, Morad Alizadeh, M. H. Tahir, Gauss M. Cordeiro, M. Mansoor, Muhammad Zubair, Gholamhossein Hamedani
The Kumaraswamy Marshal-Olkin Family Of Distributions, Morad Alizadeh, M. H. Tahir, Gauss M. Cordeiro, M. Mansoor, Muhammad Zubair, Gholamhossein Hamedani
Mathematics, Statistics and Computer Science Faculty Research and Publications
We introduce a new family of continuous distributions called the Kumaraswamy Marshal-Olkin generalized family of distributions. We study some mathematical properties of this family. Its density function is symmetrical, left-skewed, right-skewed and reversed-J shaped, and has constant, increasing, decreasing, upside-down bathtub, bathtub and S-shaped hazard rate. We present some special models and investigate the asymptotics and shapes of the family. We derive a power series for the quantile function and obtain explicit expressions for the moments, generating function, mean deviations, two types of entropies and order statistics. Some useful characterizations of the family are also proposed. The method of maximum …
Characterizations Of Levy Distribution Via Sub-Independence Of The Random Variables And Truncated Moments, Gholamhossein G. Hamedani, M. Ahsanullah, Seyed Morteza Najibi
Characterizations Of Levy Distribution Via Sub-Independence Of The Random Variables And Truncated Moments, Gholamhossein G. Hamedani, M. Ahsanullah, Seyed Morteza Najibi
Mathematics, Statistics and Computer Science Faculty Research and Publications
The concept of sub-independence is based on the convolution of the distributions of the random variables. It is much weaker than that of independence, but is shown to be sufficient to yield the conclusions of important theorems and results in probability and statistics. It also provides a measure of dissociation between two random variables which is much stronger than uncorrelatedness. Following Ahsanullah and Nevzorov (2014), we present certain characterizations of Levy distribution based on: (i) the sub-independence of the random variables; (ii) a simple relationship between two truncated moments; (iii) conditional expectation of certain function of the random variable. In …
Characterizations Of Transmuted Complementary Weibull Geometric Distribution, Gholamhossein Hamedani
Characterizations Of Transmuted Complementary Weibull Geometric Distribution, Gholamhossein Hamedani
Mathematics, Statistics and Computer Science Faculty Research and Publications
We present certain characterizations of a recently introduced distribution (Afify et al., 2014), called Transmuted Complementary Weibull Geometric distribution based on: hazard function ; a simple relation between two truncated moments. We like to mention that the characterization which is expressed in terms of the ratio of truncated moments is stable in the sense of weak convergence. It does not require a closed form for the cumulative distribution function and serves as a bridge between a first order differential equation and probability.
Characterizations Of New Modified Weibull Distribution, Gholamhossein Hamedani
Characterizations Of New Modified Weibull Distribution, Gholamhossein Hamedani
Mathematics, Statistics and Computer Science Faculty Research and Publications
Several characterizations of a New Modified Weibull distribution, introduced by Doostmoradi et al. (2014), are presented. These characterizations are based on: (i) truncated moment of a function of the random variable; (ii) the hazard function; (iii) a single function of the random variable; (iv) truncated moment of certain function of the 1st order statistic.
Remarks On A Paper Of Lee And Lim, Gholamhossein Hamedani, Michael Slattery
Remarks On A Paper Of Lee And Lim, Gholamhossein Hamedani, Michael Slattery
Mathematics, Statistics and Computer Science Faculty Research and Publications
Lee and Lim (2009) state three characterizations of Loamax, exponential and power function distributions, the proofs of which, are based on the solutions of certain second order non-linear differential equations. For these characterizations, they make the following statement : "Therefore there exists a unique solution of the differential equation that satisfies the given initial conditions". Although the general solution of their first differential equation is easily obtainable, they do not obtain the general solutions of the other two differential equations to ensure their claim via initial conditions. In this very short report, we present the general solutions of these equations …
Some Remarks On Arslan’S 2011 Paper, Gholamhossein Hamedani, Hans Volkmer
Some Remarks On Arslan’S 2011 Paper, Gholamhossein Hamedani, Hans Volkmer
Mathematics, Statistics and Computer Science Faculty Research and Publications
It is shown that the main theorem of Arslan’s paper (Theorem 2, 2011), as stated, is incorrect. Under additional conditions, we present a short proof of the corrected version of the theorem. We also give a proof of a theorem of Rao and Shanbhag (1991), employed by Arslan, without the use of the Kolmogorov Consistency Theorem.