An integrated lack of memory characterization of the exponential distribution

Summary In this note a charactrization of the exponential distribution is discussed based on yet another extension of the lack of memory property. The result was motivated by a functional equation appearing in Ahsannulah [1], [3]     

A note on the moments of order statistics from doubly truncated exponential distribution

Summary In a recent paper [2], the author has obtained some recurrence relations between the moments of order statitics from the exponential and right truncated exponential distributions. In this paper, similar relations are derived for a doubly truncated exponential distribution. It is shown that one can obtain all the moments by using these recurrence relations.     

On the exact distribution and mean value function of a geometric process with exponential interarrival times

The geometric process is considered when the distribution of the first interarrival time is assumed to be exponential. An analytical expression for the one dimensional probability distribution of this process is obtained as a solution to a system of recursive differential equations. A power series expansion is derived for the geometric renewal function by using an integral equation and evaluated in a computational perspective. Further, an extension is provided for the power series expansion of the geometric renewal function in the case of the Weibull distribution.     

Consequences of Schanuel's condition for zeros of exponential terms

Assuming “Schanuel's Condition” for a certain class of exponential fields, Sturm's technique for polynomials in real closed fields can be extended to more complicated exponential terms in the corresponding exponential field. Hence for this class of terms the exact number of zeros can be calculated. These results give deeper insights into the model theory of exponential fields. MSC: 03C65, 03C60, 12L12.     

On a characterization of the exponential distribution by spacings

Summary LetX be a non-negative random variable with probability distribution functionF. SupposeX _i,n (i=1,…,n) is theith smallest order statistics in a random sample of sizen fromF. A necessary and sufficient condition forF to be exponential is given which involves the identical distribution of the random variables (n−i)(X _i+1,n−X_i,n) and (n−j)(X _j+1,n−X_j,n) for somei, j andn, (1≦i<j<n). The work was partly completed when the author was at the Dept. of Statistics, University of Brasilia, Brazil.     

Irreducibility and the distribution of some exponential sums

We relate the distribution of the absolute value of some generalized Gauss sums to the absolute irreducibility of some polynomials in two variables in characteristic 0 and p.     

On roots of exponential terms

In the present paper some tools are given to state the exact number of roots for some simple classes of exponential terms (with one variable). The result were obtained by generalizing Sturm's technique for real closed fields. Moreover for arbitrary non-zero terms t(x) certain estimations concerning the location of roots of t(x) are given. MSC: 03C65, 03C60, 12L12.     

Linear prediction of record values for the two parameter exponential distribution

This paper deals with the problem of predicting thesth record value based on the firstm record values (s>m) when the observations are from the exponential distribution. Various estimates for thesth record value are obtained and their mean square errors are compared.     

Markov interlacing property for exponential polynomials

Let Un be an extended Tchebycheff system on the real line. Given a point , where x₁<?<xn, we denote by the polynomial from Un, which has zeros x₁,…,xn. (It is uniquely determined up to multiplication by a constant.) The system Un has the Markov interlacing property (M) if the assumption that and interlace implies that the zeros of and interlace strictly, unless . We formulate a general condition which ensures the validity of the property (M) for polynomials from Un. We also prove that the condition is satisfied for some known systems, including exponential polynomials and . As a corollary we obtain that property (M) holds true for Müntz polynomials , too.     

二元Friday-Patil型指数分布的特征及其应用

导出了二元Friday-Patil型指数分布的一个特征,利用该特征获得了二元Friday-Patil型指数分布参数的最大似然估计及矩估计,给出了强度服从二元Friday-Patil型指数分布时系统可靠度的估计.     

Pitman closeness results for Type-I censored data from exponential distribution

Recent work on Pitman closeness has compared estimators under Type-II censored samples from exponential distribution based on observed number of failures. In this paper, we carry out similar Pitman closeness comparisons for Type-I censored samples from exponential distribution based on time under test.     

Two-sided M-Bayesian credible limits of reliability parameters in the case of zero-failure data for exponential distribution

In this paper, we study the interval estimation of failure rate and reliability for exponential distribution, in the case of zero-failure data, using the method of two-sided Modified Bayesian (M-Bayesian) credible limit. We discuss the properties of two-sided M-Bayesian credible limits which include the impact of the value of upper bound c of hyper parameter, and the influence of different prior distributions of hyper parameter on two-sided M-Bayesian credible limits. The paper obtains the relationship between three kinds of two-sided M-Bayesian credible limits and two-sided classical confidence limits. Finally, we use a real data set to verify the properties of two-sided M-Bayesian credible limits, and the computing results indicate that the method is efficient and easy to operate.     

A fuzzy adaptive network approach to parameter estimation in cases where independent variables come from an exponential distribution

In a regression analysis, it is assumed that the observations come from a single class in a data cluster and the simple functional relationship between the dependent and independent variables can be expressed using the general model; Y=f(X)+ε. However; a data cluster may consist of a combination of observations that have different distributions that are derived from different clusters. When faced with issues of estimating a regression model for fuzzy inputs that have been derived from different distributions, this regression model has been termed the ‘switching regression model’ and it is expressed with . Here l_i indicates the class number of each independent variable and p is indicative of the number of independent variables [J.R. Jang, ANFIS: Adaptive-network-based fuzzy inference system, IEEE Transaction on Systems, Man and Cybernetics 23 (3) (1993) 665–685; M. Michel, Fuzzy clustering and switching regression models using ambiguity and distance rejects, Fuzzy Sets and Systems 122 (2001) 363–399; E.Q. Richard, A new approach to estimating switching regressions, Journal of the American Statistical Association 67 (338) (1972) 306–310].In this study, adaptive networks have been used to construct a model that has been formed by gathering obtained models. There are methods that suggest the class numbers of independent variables heuristically. Alternatively, in defining the optimal class number of independent variables, the use of suggested validity criterion for fuzzy clustering has been aimed. In the case that independent variables have an exponential distribution, an algorithm has been suggested for defining the unknown parameter of the switching regression model and for obtaining the estimated values after obtaining an optimal membership function, which is suitable for exponential distribution.     

Bayesian inference for Pr (Y

《Applied Mathematical Modelling》2014,38(5-6):1698-1709

Fake exponential Brownian motion

We construct a fake exponential Brownian motion, a continuous martingale different from classical exponential Brownian motion but with the same marginal distributions, thus extending results of Albin and Oleszkiewicz for fake Brownian motions. The ideas extend to other diffusions.     

On the joint distribution of Grubbs' statistics

In this paper, the joint pdf's of Grubbs' statistics for normal and exponential populations are obtained; and relationship between the two pdf's is established. New formulations of the first marginal pdf of Grubbs' statistics for these two populations are given; the formulation of the exponential population case is a new one. Iterative formulas for the pdf of Grubbs' statistics are also obtained.