This paper introduces the concept of a random variable, which is nothing more than a variable whose numeric value is determined by the outcome of an experiment. To describe the probabilities that are associated with these numeric values in a concise and conceptually useful manner, the probability distribution and probability density function are introduced. Then, the moment generating function ...

In this paper, a performance analysis of amplifyand-forward (AF) relaying cooperative diversity system with relay selection is given when all terminals are moving. We have derived analytical expressions for probability density function (PDF), cumulative distribution function (CDF) and moment generating function (MGF) of end-to-end signal-to-noise ratio (SNR) for the considered system. Then, the...

We have established in the previous lecture that under some assumptions on the Moment Generating Function (MGF) M(θ), an i.i.d. sequence of random variables Xi, 1 ≤ i ≤ n with mean μ satisfies P(Sn ≥ a) ≤ exp(−nI(a)), ; −1 where Sn = n Xi, and I(a) £ supθ(θa− log M(θ)) is the Legendre 1≤i≤n transform. The function I(a) is also commonly called the rate function in the theory of Large Deviations....

A detection method based on sensitization of a squared double differentiated signal is developed which discriminates the turbulent zones from laminar zones quite accurately. The procedure adopts a variable threshold and a variable hold time of the order of the Kolmogorov time scale. The output file so generated, includes all the information for further analysis of the turbulent signal.

Moment invariants are one of the techniques of feature extraction frequently used for pattern recognition algorithms. A moment is a projection of function into polynomial basis and an invariant is a function returning the same value for an input with and without particular class of degradation. Several techniques of moment invariant creation exist often generating over-complete set of invariant...

This paper introduced a new life time data analysis distribution name three parameters quasi gamma discussed about its some properties including moment generating function, rth origin and mean, mean deviations, reliability measurements, Bonferroni Lorenz curve, Order statistics, Renyi entropy, also maximum likelihood method real-life applications.

We provide a recursive formula for the computation of moments distributions belonging to subclass exponential family. This includes important cases as binomial, negative Poisson, gamma and normal distribution, among others. The provides procedure sequentially calculate using only elementary operations. approach makes no use moment generating function.

In this paper explicit expressions and some recurrence relations are derived for marginal and joint moment generating functions of generalized order statistics from Erlang-truncated exponential distribution. The results for k-th record values and order statistics are deduced from the relations derived. Further, a characterizing result of this distribution on using the conditional expectation of...

In this paper, a class of multivariate skew distributions has been explored. Then its properties are derived. The relationship between the multivariate skew normal and the Wishart distribution is also studied. @ 2003 Elsevier Science Ltd. All rights reserved. Keywords-Skew normal distribution, Wishart distribution, Moment generating function, Moments. Skewness.

This paper describes the construction of a lower bound for the tails of general random variables, using solely knowledge of their moment generating function. The tilting procedure used allows for the construction of lower bounds that are tighter and more broadly applicable than existing tail approximations.