Weighted Gamma (WG), a weighted version of Gamma distribution, is introduced. The hazard function is increasing or upside-down bathtub depending upon the values of the parameters. This distribution can be obtained as a hidden upper truncation model. The expressions for the moment generating function and the moments are given. The non-linear equations for finding maximum likelihood estimators (M...

Conditions under which a naive algebraic solution to a random affine stochastic equation yields a genuine stochastic solution with a given independence property are derived. The well-known example by Letac is characterized and generalized to a non-trivial dependence structure. As by-products, a series representation of the exact probability density of a sum of independent gamma random variables...

We study a new class of time inhomogeneous Pólya-type urn schemes and give optimal rates of convergence for the distribution of the properly scaled number of balls of a given color to nearly the full class of generalized gamma distributions with integer parameters, a class which includes the Rayleigh, half-normal and gamma distributions. Our main tool is Stein’s method combined with characteriz...

background: polymer gel dosimetry is still the only dosimetry method for direct measuring of threedimensional dose distributions. mri polymer gel dosimeters are tissue equivalent and can act as a phantom material. in this study the obtained isodose maps with pagat polymer gel dosimeter were compared to those calculated with egsnrs for singleshot irradiations of 8 and 18 mm collimators of gamma ...

Dirichlet distribution is a kind of high-dimensional continuous probability distribution, which has important applications in the fields statistics, machine learning and bioinformatics. In this paper, based on gamma we study two two-dimensional random variables. Then derive properties these variables by using non-central confluent hypergeometric series. From properties, find follow generalized ...

We study a new class of time inhomogeneous Pólya-type urn schemes and give optimal rates of convergence for the distribution of the properly scaled number of balls of a given color to nearly the full class of generalized gamma distributions with integer parameters, a class which includes the Rayleigh, half-normal and gamma distributions. Our main tool is Stein’s method combined with characteriz...

We present a novel statistical model, the generalized-Gaussian-Rician (GG-Rician) distribution, for characterization of synthetic aperture radar (SAR) images. Since accurate models lead to better results in applications such as target tracking, classification, or despeckling, characterizing SAR images various scenes including urban, sea surface, agricultural is essential. The proposed model bas...

In general, the distribution of residuals cannot be obtained explicitly. We give an asymptotic formula for the density of Pearson residuals in continuous generalized linear models corrected to order n−1, where n is the sample size. We define corrected Pearson residuals for these models that, to this order of approximation, have exactly the same distribution of the true Pearson residuals. Applic...

using the hyers-ulam-rassias stability method, weinvestigate isomorphisms in banach algebras and derivations onbanach algebras associated with the following generalized additivefunctional inequalitybegin{eqnarray}|af(x)+bf(y)+cf(z)|  le  |f(alpha x+ beta y+gamma z)| .end{eqnarray}moreover, we prove the hyers-ulam-rassias stability of homomorphismsin banach algebras and of derivations on banach ...