abstract in recent years, many researchers have attempted to estimate the soil hydraulic functions (e.g. soil moisture characteristics curve, and hydraulic conductivity function) using particle-size distribution (psd) curve. in these studies, an accurate mathematical representation of psd is required for fitting the observed data. so far, some mathematical models were developed with different l...

In [1] we uniquely introduced ultra exponential functions (uxpa) and denednext step of the serial binary operations: addition, multiplication and power.Also, we exhibited the topic of limit summability of real functions in [2,3]. Inthis paper, we study limit summability of the ultra exponential functions andprove some of their properties. Finally, we pose an unsolved problem aboutthem.

In this paper, we present an integrodifferential diffusion equation for continuous-time random walk that is valid for a generic waiting time probability density function. Using this equation, we also study diffusion behaviors for a couple of specific waiting time probability density functions such as exponential and a combination of power law and generalized Mittag-Leffler function. We show tha...

Currently, much research attention has focused on generalizations of known mathematical objects in order to obtain adequate models describing real phenomena. An important role the applied theory probability and statistics is gamma class distributions, which proven be a convenient effective tool for modeling many processes. The quite wide includes distributions that have useful properties such a...

Abstract In this paper, two modified, design-based calibration ratio-type estimators are presented. The suggested were developed under stratified random sampling using information on an auxiliary variable in the form of robust statistical measures, including Gini’s mean difference, Downton’s method and probability weighted moments. properties (biases MSEs) proposed studied up to terms first-ord...

Natural exponential families of distributions have probability mass functions of the form [exp(Ox)]#(dx) where # is a given measure, and 0 > 0 is a parameter. When we compute the mean and the variance, and force the variance to be a quadratic function of the mean as 0 is varied, the number of families becomes severely restricted. Morris (1982) showed that there are in fact only six natural expo...