Estimation of raindrop size distribution over large spatial and temporal scales has been a long-standing goal of polarimetric radar. Algorithms to estimate the parameters of a gamma raindrop size distribution model from polarimetric radar observations of reflectivity, differential reflectivity, and specific differential phase are developed. Differential reflectivity is the most closely related ...

The ROC (Receiver Operating Characteristics) curves are frequently used to measure the effectiveness of diagnostic biomarkers. A global measure of the ROC curve is the Youden index, the maximum difference between sensitivity and 1-specificity. The cut-point is the value for which the maximum is attained. In this paper we obtain the asymptotic distribution of the optimal cut-point under the assu...

From a suitable integral representation of the Laplace transform of a positive semi–definite quadratic form of independent real random variables with not necessarily identical densities a univariate integral representation is derived for the cumulative distribution function of the sample variance of i.i.d. random variables with a gamma density, supplementing former formulas of the author. Furth...

In the evaluation of structural reliability, a failure is defined as the event in which stress exceeds a resistance that is liable to deterioration. This paper presents a method to combine the two stochastic processes of deteriorating resistance and fluctuating load for computing the time-dependent reliability of a structural component. The deterioration process is modelled as a gamma process, ...

A new method is required for change-point testing of precipitation data that is capable of applying valid precipitation models. First, stochastic precipation models are researched and classified. Typically, the occurrence of rain is modeled using a two-state, first-order Markov chain, and the intensity of rain is modeled using a two-parameter gamma distribution. Using the likelihood ratio test ...

We consider stochastic particle acceleration in plasmas around stellar mass black holes to explain the emissions above 1 MeV from Galactic black hole candidates. We show that for certain parameter regimes, electrons can overcome Coulomb losses and be accelerated beyond the thermal distribution to form a new population, whose distribution is broad and usually not a power law; the peak energy of ...

Extreme value theory for the maximum of a time series of daily precipitation amount is described. A chain-dependent process is assumed as a stochastic model for daily precipitation, with the intensity distribution being the gamma. To examine how the e€ective return period for extreme high precipitation amounts would change as the parameters of the chain-dependent process change (i.e., probabili...