Let ξ be a (possibly killed) subordinator with Laplace exponent φ and denote by Iφ = ∫∞ 0 e−ξsds, the so-called exponential functional. Consider the positive random variable Iψ1 whose law, according to Bertoin and Yor [6], is determined by its negative entire moments as follows E[I ψ1 ] = n ∏ k=1 φ(k), n = 1, 2 . . . . In this note, we show that Iψ1 is a positive self-decomposable random variab...

In this paper we give generalization of Opial-type inequalities by using generalized fractional integral operator involving generalized Mittag–Leffler function. We deduce some results which already have been proved. Also we consider n -exponential convexity of some non-negative differences of inequalities involving Mittag-Leffler function and deduce their exponential convexity and log-convexity.

Abstract. Among the fastest methods for solving stiff PDE are exponential integrators, which require the evaluation of , where is a negative semidefinite matrix and is the exponential function or one of the related “ functions” such as . Building on previous work by Trefethen and Gutknecht, Minchev, and Lu, we propose two methods for the fast evaluation of that are especially useful when shifte...

This paper discusses the characteristics of the exponential distribution and the related distribution functions including gamma, weibull and lognormal then relates some of their properties to the application of Markov models. One of the major properties is forgetfulness, the consequence of this is that Markov and stationarity assumptions imply that the times between events must be negative-expo...

BACKGROUND Several studies have shown that total depressive symptom scores in the general population approximate an exponential pattern, except for the lower end of the distribution. The Center for Epidemiologic Studies Depression Scale (CES-D) consists of 20 items, each of which may take on four scores: "rarely," "some," "occasionally," and "most of the time." Recently, we reported that the it...

Kingdom (present address) – 2 – ABSTRACT Using an Eulerian perturbative calculation, we show that the distribution of relative pairwise velocities which arises from gravitational instability of Gaussian density fluctuations has asymmetric (skewed) exponential tails. The negative skewness is induced by the negative mean streaming velocity of pairs (the infall prevails over expansion), while the ...

We measure the distribution of intensity of microwave radiation transmitted through absorbing random waveguides of lengths L up to localization length xi . For large intensity values the distribution is given by a negative stretched exponential to the 1/2 power, in agreement with predictions by Nieuwenhuizen and van Rossum [Phys. Rev. Lett. 74, 2674 (1995)] for diffusing waves in nonabsorbing s...

This paper has a focus on non-stationary time series formed from small non-negative integer values which may contain many zeros and may be over-dispersed. It describes a study undertaken to compare various suitable adaptations of the simple exponential smoothing method of forecasting on a database of demand series for slow moving car parts. The methods considered include simple exponential smoo...