Abstract: We analyze the (unconditional) distribution of a linear predictor that is constructed after a data-driven model selection step in a linear regression model. First, we derive the exact finite-sample cumulative distribution function (cdf) of the linear predictor, and a simple approximation to this (complicated) cdf. We then analyze the large-sample limit behavior of these cdfs, in the f...

Different functions, each in the form of a modified Weibull cumulative distribution function (cdf), were joined together to form a segmented cdfto approximate diameter distributions in forest stands. Estimates of five percentile points (the 0th, 25th, 50th, 75th, and 100th percentiles) were used to determine a segmented cdf. The segmented cdf and the Weibull distribution were fit to diameter da...

In this paper the most important statistical metrics of the product and the ratio of two correlated Generalized Gamma (GG) random variables (RV)s, raised to an arbitrary power, are studied. The probability density function (PDF) and the cumulative distribution function (CDF) have been derived in most cases in closed form. Moreover, an upper bound for the CDF of the sum of the two correlated GG ...

-In this paper, the k-μ random variable will be considered and closed form expressions for probability density function (PDF), cumulative distribution function (CDF) and moments for this distribution will be derived. Also, product, ratio, maximum and minimum of two k-μ random variables will be studied and PDFs of these functions calculated in the closed forms. Then, obtained statistical functio...

Abstract Cantor sets are constructed from iteratively removing sections of intervals. This process yields a cumulative distribution function (CDF), the invariant Borel probability measure associated with their iterated systems. Under appropriate assumptions, we identify sampling schemes such CDFs, meaning that underlying set can be reconstructed sufficiently many samples its CDF. To this end, p...

The computation of the cumulative distribution (cdf), the complementary cdf (ccdf), and the density of certain shot-noise random variables is discussed. After subtracting oo a few terms that can be computed in closed form, what remains can be approximated by a general method for approximating samples of a cdf or ccdf by summing a Fourier series whose coeecients are modulated samples of their ch...

Many problems of enzyme kinetics can be described by a function known as the Michaelis-Menten (M-M) function. In this paper, motivated by the importance of Michaelis-Menten function in biochemistry and other biological phenomena, we have introduced a new class of generalized Pearson distribution arising from Michaelis-Menten function. Various properties of this distribution are derived, for exa...

Distributions have several different types of associated functions. The most familiar is the density function. Figure 1A and 1D show density functions for the normal distribution and gamma distribution, respectively. Density functions are related to histograms in that if enough data are collected then the histogram and density share the same shape. Hence, density functions serve as a first-orde...

The method of distributions is developed for systems that are governed by hyperbolic conservation laws with stochastic forcing. yields a deterministic equation the cumulative distribution function (CDF) system state, e.g., flow velocity an inviscid Burgers random source coefficients. This achieved without recourse to any closure approximation. CDF model verified against Monte Carlo (MC) simulat...

Due to the widespread applicability and use of normal distribution, a need has arisen approximate its cumulative distribution function (cdf). In this article, five new simple approximations standard cdf are developed. order assess accuracy proposed approximations, both maximum absolute error mean were used. The errors lie between 0.00095 0.00946, which is highly accurate if compared existing qu...