Search results for " Probability distributions"
showing 10 items of 10 documents
Bartlett formalism generating functions and Z-transforms in fluctuation and noise theory
1983
Abstract “La theorie des fonctions generatrices s'adapte elle meme et avec la plus grande generalite aux questions des probabilite les plus difficiles.” (Laplace, 1812) “An important part of probability theory consists of the derivation of the probability distribution of the sum of n random variables, each of which obeys a given probability law, and the development of asymptotic forms of these distributions valid for increasing n. Probability generating functions owe their dominant position to the simplification they permit to both problems. Their employment to obtain the successive moments of a probability distribution and to solve the difference equations of probability theory is ancillar…
Applying a probabilistic model of rainfall and snow days occurrence to daily series recorded in NW Italy.
2014
Daily precipitation records exist spanning several decades. A valuable amount of climatic information exists in the time-series of interarrival times (IT), defined as the succession of times (number of days) elapsed from a rainy (or snowy) day to the one immediately preceding it.In a previous work, Agnese et al. (2014) have been successfully tested some probabilistic modelling of rain occurrence on Sicily rainfall data; particularly, the better fitting of IT’s observed frequencies was obtained by 3-parameter Lerch-series distribution. In this work thisdistribution is tested on 70 years of 20 precipitation time-series taken in the North-West Italy, both in the plain and in the mountains, up …
Statistical distribution of soil loss and sediment yield at Sparacia experimental area, Sicily
2010
Abstract An analysis of the statistical distribution of event soil loss was carried out using the data collected in the period 1999–2008 at the microplots and plots of the Sparacia experimental area (Sicily, Italy). For a given microplot size, the analysis allowed to establish that the soil loss frequency distribution was skewed. Using the soil loss normalized by the event mean value, the analysis also showed that the frequency distributions corresponding to different microplot and plot sizes were overlapping, i.e. all distributions were extracted by the same statistical population. The developed analysis allowed to suggest that the soil loss of a given return period can be estimated using …
Establishing a soil loss threshold for limiting rilling
2015
In this paper a frequency analysis of event soil loss measurements collected in the period 1999–2012 at the microplots and plots of the Sparacia Experimental Area in Sicily, southern Italy, was developed. The analysis was carried out using the annual maximum soil loss measurements normalized by the mean soil loss measured at a given temporal and spatial scale. The empirical frequency distribution of the normalized variable was well fitted by two Gumbel’s theoretical probability distributions discriminated by a value of the normalized variable equal to 2. This last value discriminates between the relatively low and frequent values of the normalized variable and the high and rare ones. The an…
Modelling the occurrence of rainy days under a typical Mediterranean climate
2014
The statistical inference of the alternation of wet and dry periods in daily rainfall records can be achieved through the modelling of inter-arrival time-series, IT, defined as the succession of times elapsed from a rainy day and the one immediately preceding it. In this paper, under the hypothesis that ITs are independent and identically distributed random variables, a modelling framework based on a generalisation of the commonly adopted Bernoulli process is introduced. Within this framework, the capability of three discrete distributions, belonging to the Hurwitz–Lerch-Zeta family, to reproduce the main statistical features of IT time-series was tested. These distributions namely Lerch-se…
Radon transform as a set of probability distributions
2009
It is proved that the Radon transform of the Wigner function gives the probability distributions related to measuring the observable operators obtained as linear combinations of position and momentum of the relevant particle. The generalization to an arbitrary number of degrees of freedom is given.
A characterization of the distribution of a weighted sum of gamma variables through multiple hypergeometric functions
2008
Applying the theory on multiple hypergeometric functions, the distribution of a weighted convolution of Gamma variables is characterized through explicit forms for the probability density function, the distribution function and the moments about the origin. The main results unify some previous contributions in the literature on nite convolution of Gamma distributions. We deal with computational aspects that arise from the representations in terms of multiple hypergeometric functions, introducing a new integral representation for the fourth Lauricella function F (n) D and its con uent form (n) 2 , suitable for numerical integration; some graphics of the probability density function and distr…
Understanding 802.11e contention-based prioritization mechanisms and their coexistence with legacy 802.11 stations
2005
The IEEE 802.11e task group has reached a stable consensus on two basic contention-based priority mechanisms to promote for standardization: usage of different arbitration interframe spaces and usage of different minimum/maximum contention windows. The goal of this article is to provide a thorough understanding of the principles behind their operation. To this purpose, rather than limit our investigation to high-level (e.g. throughput and delay) performance figures, we take a closer look at their detailed operation, also in terms of low-level performance metrics (e.g., the probability of accessing specific channel slots). Our investigation on one hand confirms that AIFS differentiation prov…
Using plot soil loss distribution for soil conservation design
2011
Abstract Soil conservation design is generally based on the estimation of average annual soil loss but it should be developed taking into account storms of a given return period. However, use of frequency analysis in soil erosion studies is relatively limited. In this paper, an investigation on statistical distribution of soil loss measurements was firstly carried out using a relatively high number of simultaneously operating plots of different lengths, λ (11, 22, 33 and 44 m) at the experimental station of Sparacia (southern Italy). Using a simple normalization technique, the analysis showed that the probability distribution of the normalized soil loss is independent of both the scale leng…
On the accuracy of three statistical softwares
2005
In this paper we compare the accuracy of three packages that are commonly used for statistical calculations: Excel of Microsoft, version XP Edition 2003, Statistica of Statsoft, version 6, and R, an open-source free software, available on the web, version 1.9.0. To assess the accuracy of each software in different statistical areas, we are going to use benchmarks expressly developed for this aim. The obtained results show a superiority of R in comparison with the other two softwares.