This study presents a dynamic way in a DG planning problem instead of the last static or pseudo-dynamic planning point of views. A new way in modeling the DG units’ output power and the load uncertainties based on the probability rules is proposed in this paper. A sensitivity analysis on the stochastic nature of the electricity price and global fuel price is carried out through a proposed model...

This article discusses statistical models for solar flare interval distribution in individual active regions. We analyzed solar flare data in 55 active regions that are listed in the Geosynchronous Operational Environmental Satellite (GOES) soft X-ray flare catalog for the years from 1981 to 2005. We discuss some problems with a conventional procedure to derive probability density functions fro...

Probabilistic methods involving maximum-likelihood parameter estimation have become a powerful tool in computational crystallography. At the centre of these methods are the relevant probability distributions. Here, equations are developed based on the complex multivariate normal distribution that generalize the distributions currently used in maximum-likelihood model and heavy-atom refinement. ...

-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...

We introduce in this paper a new four-parameter generalized version of the linear failure rate distribution which is called Beta-linear failure rate distribution. The new distribution is quite flexible and can be used effectively in modeling survival data and reliability problems. It can have a constant, decreasing, increasing and bathtub-shaped failure rate function depending on its parameter...

The spatial orientation of vectors rigidly embedded in polymer chains are described in terms of time-dependent joint probability distribution functions. Serial expansion in terms of double spherical harmonics is adopted for the probability distribution functions, with the coefficients therein evaluated from Brownian dynamics simulations. Truncation of the series after the second-order harmonics...

Cryptography and simulation of systems require that events of pre-defined probability be generated. This paper presents methods to generate target probability events based on the oblivious transfer protocol and target probabilistic sequences using probability distribution functions.

1 Last two lectures ¯ probability spaces ¯ probability measure ¯ random variables and stochastic processes ¯ distribution functions ¯ independence ¯ conditional probability ¯ memoriless property of geometric and exponential distributions ¯ expectation ¯ conditional expectation (double expectation) ¯ mean-square estimation 1

We show that the generating functions of the generalized Catalan numbers can be identified with the moment generating functions of probability density functions related to the Brownian motion stochastic process. Specifically, the probability density functions are exponential mixtures of inverse Gaussian (EMIG) probability density functions, which arise as the first passage time distributions to...