Related papers: An exactly solvable record model for rainfall

Semi-continuous data comes from a distribution that is a mixture of the point mass at zero and a continuous distribution with support on the positive real line. A clear example is the daily rainfall data. In this paper, we present a novel…

We obtain a strong law of large numbers and a functional central limit theorem, as $t\to\infty$, for the number of records up to time $t$ and the Lebesgue measure (length) of the subset of the time interval $[0,t]$ during which the Poisson…

The record statistics of complex random states are analytically calculated, and shown that the probability of a record intensity is a Bernoulli process. The correlation due to normalization leads to a probability distribution of the records…

Rainfall exhibits extreme variability at many space and time scales and calls for a statistical description. Based on an analysis of radar measurements of precipitation over the tropical oceans, we introduce a new probability law for the…

Numerous weather parameters affect the occurrence and amount of rainfall. Therefore, it is important to study these parameters and their interdependency. In this paper, different weather and time-related variables -- relative humidity,…

Using techniques from Poisson approximation, we prove explicit error bounds on the number of permutations that avoid any pattern. Most generally, we bound the total variation distance between the joint distribution of pattern occurrences…

There are two main quantities involved in the deviation of a stochastic process from a Poisson process: the squared coefficient of variation of the time intervals between adjacent events and the Fano factor of the number of reaction events.…

We propose a new statistical protocol for the estimation of precipitation using lightning data. We first identify rainy events using a scan statistics, then we estimate Rainfall Lighting Ratio (RLR) to convert lightning number into rain…

We show that the universal properties of the rainfall phenomenon are the scaling properties of the probability density function of inter-drop intervals during quiescent periods, time intervals of sparse precipitation, and the universal…

Count time series are widely encountered in practice. As with continuous valued data, many count series have seasonal properties. This paper uses a recent advance in stationary count time series to develop a general seasonal count time…

We investigate how the statistics of extremes and records is affected when taking the moving average over a window of width $p$ of a sequence of independent, identically distributed random variables. An asymptotic analysis of the general…

One of the key clues to consider rainfall as a self-organized critical phenomenon is the existence of power-law distributions for rain-event sizes. We have studied the problem of universality in the exponents of these distributions by means…

We say that a string of length $d$ occurs, in a Bernoulli sequence, if a success is followed by exactly $(d-1)$ failures before the next success. The counts of such $d$-strings are of interest, and in specific independent Bernoulli…

Highly resoluted and accurate daily precipitation data are required for impact models to perform adequately and to correctly measure high-risk events' impact. In order to produce such data, bias-correction is often needed. Most of those…

Due to complex physical phenomena, the distribution of heavy rainfall events is difficult to model spatially. Physically based numerical models can often provide physically coherent spatial patterns, but may miss some important…

We consider a random walk on the fully-connected lattice with $N$ sites and study the time evolution of the number of distinct sites $s$ visited by the walker on a subset with $n$ sites. A record value $v$ is obtained for $s$ at a record…

This paper describes a compound Poisson-based random effects structure for modeling zero-inflated data. Data with large proportion of zeros are found in many fields of applied statistics, for example in ecology when trying to model and…

Local perturbations in conservative particle systems can have a non-local influence on the stationary measure. To capture this phenomenon, we analyze in this paper two toy models. We study the symmetric exclusion process on a countable set…

Precipitation data collected at sub-hourly resolution represents specific challenges for missing data recovery by being largely stochastic in nature and highly unbalanced in the duration of rain vs non-rain. Here we present a two-step…

In the context of this paper, a record is an entry in a sequence of random variables (RV's) that is larger or smaller than all previous entries. After a brief review of the classic theory of records, which is largely restricted to sequences…