a r t i c l e i n f o Probability distribution functions (PDF) can be useful descriptors for the random structure of non-crystalline solids. The lognormal PDF has provided a good description of the distribution of interstitial site sizes in non-crystalline solids, both metallic and nonmetallic. The utility of this descriptor to characterize the ring statistics of vitreous silica under a wide ra...

The Lorenz curve for assessing economic inequality depicts the relation between two cumulative distribution functions (CDFs), one for the distribution of incomes or wealth and the other for their first-moment distribution. By contrast, the receiver operating characteristic (ROC) curve for evaluating diagnostic systems depicts the relation between the complements of two CDFs, one for the distrib...

In this paper, we present an accurate approach for the estimation of statistical distribution of leakage power consumption in the presence of process variations in nano-scale CMOS technologies. The technique, which is additive with respect to the individual gate leakage values, employs Generalized Extreme Value (GEV) distribution. Compared to the previous methods based on (two-parameter) lognor...

We examine the shape of primordial black hole mass distribution arising from a peak in power spectrum. In light improvements to modeling, we revisit claim that effects critical collapse produce is not described by commonly assumed lognormal, showing this conclusion remains valid, particularly for narrow peaks where insensitive properties and determines minimum width. propose some alternative mo...

Two concepts of symmetry for the distributions of positive random variables Y are log-symmetry (symmetry of the distribution of log Y ) and Rsymmetry (Mudholkar & Wang, 2007). In this paper, we characterise the distributions that have both properties, which we call doubly symmetric. It turns out that doubly symmetric distributions constitute a subset of those distributions that are moment-equiv...

Two concepts of symmetry for the distributions of positive random variables Y are log-symmetry (symmetry of the distribution of log Y ) and Rsymmetry (Mudholkar & Wang, 2007). In this paper, we characterise the distributions that have both properties, which we call doubly symmetric. It turns out that doubly symmetric distributions constitute a subset of those distributions that are moment-equiv...

We show that if the intrinsic break energy of Gamma-Ray Bursts (GRBs) is determined by the product of more than three random variables the observed break energy distribution becomes almost lognormal including the redshift effect because of the central limit theorem. The excess from the lognormal distribution at the low break energy is possibly due to the high redshift GRBs. The same argument ma...

Two concepts of symmetry for the distributions of positive random variables Y are log-symmetry (symmetry of the distribution of log Y ) and Rsymmetry (Mudholkar & Wang, 2007). In this paper, we characterise the distributions that have both properties, which we call doubly symmetric. It turns out that doubly symmetric distributions constitute a subset of those distributions that are moment-equiv...

To evaluate the distribution function of a sum of lognormal random variables. it is common to use approximation methods based on moment matching. These include the classical and simple Fenton-Wilkinson method, which approximates the sum with a single lognormal variable, having the first two moments matched. In this letter, we give a closed-form bound for the error of the distribution function, ...