In this paper an attempt has been made to present a unified theory of the classical statistical distributions associated with generalized beta and gamma distributions of one variable. The probability density function is taken in terms of the Multivariable H-function. In particular, the characteristic function and the distribution function are investigated.

Gamma regression is a member of generalized liner models and often used when the phenomenon under study is skewed and the mean is proportional to the standard deviation. It can find applications in several areas such as life-testing problems, forecasting cancer incidences, weather extremes and quality control. Also it is a natural candidate when modeling the variance and it has been increasingly used over the past decade. paper attempts to introduce readers with the concept of the gamma regression model, in which the dependent variable has the gamma distribution, and the use of the paired bootstrapping resampling associated with the "boot" package in R program. Three confidence intervals were computed.

Assignment problem is an important problem in mathematics and is also discuss in real physical world.

Plants, animals and humans live in close association with microbial organisms. Increasingly, biologists have come to appreciate that microbes make up an important part of an organism's phenotype. This microbial community contains a unique complexity that makes it difficult to study their diversity. However, for many questions on the structure of the microbial community one only needs to know the relative order of diversity among samples rather than the total diversity. Unfortunately the culture of microorganisms can be complex but this has prompted the development of new scientific methodologies for their study. One of these methodologies is metagenomics. An important problem in metagenomics is measuring the dissimilarity between distributions of features, such as taxons or groups. The focus of this note is the proposal of a new method based on using Bhattacharyya distance and establishing a priori groups using the partitioning around medoids algorithm (PAM). The results reveal a good reduction in the size of the dataset and an interesting way of revealing possible subgroups "a priori" or communities among the microorganisms that make up the analyzed sample.

In this study the decay of temperature fluctuations in homogeneous turbulence before the final period is analyzed by using the correlation equations for fluctuating quantities at four point in the flow field. Throughout this work three-and four point-correlation equations are obtained. The correlation equations are converted into spectral form by their Fourier-transform. The set of equations are made to determinate by neglecting the quintuple correlations in comparison to the fourth-order correlation terms. Finally by integration of the energy spectrum over all wave numbers, we have obtained the decay of energy of temperature fluctuations for four point correlations. The obtained results have been shown by graphically at different Prandtl No. and at the different state of temperature. We also determined the values of the constant appear at the energy equation (

The present theory of consistent estimators of the parameters of statistical structures of homogeneous Gaussian fields can be used, for example, in the reliability predication of different engineering designs. In the paper there are discussed Gaussian homogeneous fields statistical structures