A NOTE ON PROPERTIES OF EXPONENTIAL POWER DISTRIBUTION

The most common generalization of the normal, Kotz-symmetric and double exponential distribution functions was the exponential power distribution. This distribution had been found useful in modeling real life data as studied in the literature. The present study found it necessary to fill the void in the literature by presenting some properties which characterized exponential power distribution and further made it useful in applications.

Stochastic Description of Loads on the Steel Storage Capacities

This paper deals with the study of stochastic parameters of external loads, which are used in the tasks of determining the level of reliability of steel storage capacities. To describe the random load process, the normal law and the double exponential distribution of Gumbel were used. It was formulated the technique of transition from the study of the entire random process to the consideration of its maximums. It was obtained quantitative values of the stochastic characteristics of snow and wind loads on the territory of Ukraine, without reference to the zoning maps. A general procedure for determining the probability of failure was formulated, depending from a given characteristic maximum. This index corresponds to the basic level of load. The average intersection of this level by a random load process is equal to one. Analytical formulas are obtained to determine the scale and position of the double exponential distribution of Gumbel, which depend on the characteristic maximum, as well as formulas, which help to calculate the statistical characteristics (standard, expected value and coefficient of variation) of the random value of the load maximums. The possibility of using this approach is theoretically confirmed when the density distribution of the ordinate of a random process follows the normal law. It was proposed expressions for the parameters of the distribution maximums of the random processes, which are described by the polynomial exponent and the Weibull law.

Bayes Estimation under Conjugate Prior for the Case of Laplace Double Exponential Distribution

The Bayesian estimation approach is a non-classical device in the estimation part of statistical inference which is very useful in real world situation. The main objective of this paper is to study the Bayes estimators of the parameter of Laplace double exponential distribution. In Bayesian estimation loss function, prior distribution and posterior distribution are the most important ingredients. In real life we try to minimize the loss and want to know some prior information about the problem to solve it accurately. The well known conjugate priors are considered for finding the Bayes estimator. In our study we have used different symmetric and asymmetric loss functions such as squared error loss function, quadratic loss function, modified linear exponential (MLINEX) loss function and non-linear exponential (NLINEX) loss function. The performance of the obtained estimators for different types of loss functions are then compared among themselves as well as with the classical maximum likelihood estimator (MLE). Mean Square Error (MSE) of the estimators are also computed and presented in graphs. The Chittagong Univ. J. Sci. 40 : 151-168, 2018

Bootstrapping and double-exponential limit laws

Combinatorics International audience We provide a rather general asymptotic scheme for combinatorial parameters that asymptotically follow a discrete double-exponential distribution. It is based on analysing generating functions Gh(z) whose dominant singularities converge to a certain value at an exponential rate. This behaviour is typically found by means of a bootstrapping approach. Our scheme is illustrated by a number of classical and new examples, such as the longest run in words or compositions, patterns in Dyck and Motzkin paths, or the maximum degree in planted plane trees.