We present a class of graphical models for directly representing the joint cumulative distribution function (CDF) of many random variables, called cumulative distribution networks (CDNs). Unlike graphs for probability density and mass functions, in a CDN, the marginal probabilities for any subset of variables are obtained by computing limits of functions in the model. We will show that the cond...

Very recently, extended fractional cumulative residual entropy (EFCRE) has been proposed by Foroghi et al., (2022). In this paper, we introduce past (EFCPE), which is a dual of the EFCRE. The newly measure depends on logarithm order and distribution function (CDF). Various properties EFCPE have explored. This to bivariate setup. Furthermore, conditional studied some its are provided. for inacti...

The Cox-Ingersoll-Ross model (CIR model) [2] has been a benchmark in finance for many years because of its analytical and structural tractability. The wide applications and extensions of the CIR model requires to evaluate the cumulative distribution function (CDF) of the integrated CIR process in financial modelling. As in many situations the characteristic function of the integrated CIR proces...

The main question we would like to address in this paper is as follows: Given a geometric Brownian motion (GBM) the underlying stock price model, what cumulative distribution function (CDF) for trading profit or loss, call it g(t), when an affine feedback control strategy with stop-loss order considered? Moreover, possible obtain closed-form characterization desired CDF g(t) so that theoreticia...

1. Abstract We propose a reliability analysis (RA) method that obtains the probability of failure by sequentially approximating the cumulative distribution function (CDF). This method uses the concept of the first order reliability method (FORM) in estimating the probability of failure but does not solve the optimization problem to obtain the most probable point (MPP). The goal of the proposed ...

<span lang="EN-CA">Estimating wind speed characteristics plays an essential role in designing a power plant at selected location. In this study, the Weibull, gamma, and exponential distribution models were proposed to estimate analyze parameters functions. Real measured data collected from Medan City, Indonesia. The scale shape factors of for three years calculated. observed cumulative pr...

An improved nonparametric estimator of the cumulative distribution function (CDF) and the survival function is proposed using infinite-order kernels. Fourier transform theory on generalized functions is utilized to obtain the improved bias estimates. The new estimators are analyzed in terms of their relative deficiency to the empirical distribution function and Kaplan-Meier estimator, and even ...

Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 General Probability Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Conditional Probability . . . . . . . . . . . . . . . . . . . . . . . ...

Let X be a non-negative random variable (r.v.) with cumulative distribution function (cdf) F. Suppose X(r, n,m, k), (r = 1, 2, . . . , n), m is a real number and k ≥ 1, is the rth smallest generalized order statistic. Several distributional properties of the generalized order statistics from exponential distribution are given. Some characterizations of the exponential distribution based on the ...

By using the independence structure of points following a determinantal point process, we study the radii of the spherical ensemble, the truncation of the circular unitary ensemble and the product ensemble with parameter n and k. The limiting distributions of the three radii are obtained. They are not the Tracy-Widom distribution. In particular, for the product ensemble, we show that the limiti...