Related papers: Statistics of Superior Records
In the binary hypothesis testing problem, it is well known that sequentiality in taking samples eradicates the trade-off between two error exponents, yet implementing the optimal test requires the knowledge of the underlying distributions,…
An increasing sequence $(a_n)$ of positive integers which satisfies $\frac{a_{n+1}}{a_n}>1+\eta$ for some positive $\eta$ is called a lacunary sequence. It has been known for over twenty years that every lacunary sequence is strong sweeping…
Statistical laws describe regular patterns observed in diverse scientific domains, ranging from the magnitude of earthquakes (Gutenberg-Richter law) and metabolic rates in organisms (Kleiber's law), to the frequency distribution of words in…
Statistical analysis is a major aspect of baseball, from player averages to historical benchmarks and records. Much of baseball fanfare is based around players exceeding the norm, some in a single game and others over a long career. Career…
Motivated by the study of deletion channels, this work presents improved bounds on the number of subsequences obtained from a binary sting X of length n under t deletions. It is known that the number of subsequences in this setting strongly…
We study extremal statistics and return intervals in stationary long-range correlated sequences for which the underlying probability density function is bounded and uniform. The extremal statistics we consider e.g., maximum relative to…
A probability measure $P_n$ on the symmetric group ${\mathfrak S}_n$ is said to be record-dependent if $P_n(\sigma)$ depends only on the set of records of a permutation $\sigma\in{\mathfrak S}_n$. A sequence $P=(P_n)_{n\in{\mathbb N}}$ of…
We explore some aspects of the relationship between biological evolution processes and the mathematical theory of records. For Eigen's quasispecies model with an uncorrelated fitness landscape, we show that the evolutionary trajectories…
In this paper, the key objects of interest are the sequential covariance matrices $\mathbf{S}_{n,t}$ and their largest eigenvalues. Here, the matrix $\mathbf{S}_{n,t}$ is computed as the empirical covariance associated with observations…
Measuring the concentration of random variables is a fundamental concept in probability and statistics. Here, we explore a type of concentration measure for continuous random variables with bounded support and use it to provide a notion of…
A statistical measure is given expressing relative occurrences of quantities within a given data set. Application of this measure on several real life physical data sets and some abstract distributions are shown to yield consistent results.…
This paper develops upper and lower bounds for the probability of Boolean expressions by treating multiple occurrences of variables as independent and assigning them new individual probabilities. Our technique generalizes and extends the…
Let S be a finite, ordered alphabet, and let x = x_1 x_2 ... x_n be a string over S. A "secondary index" for x answers alphabet range queries of the form: Given a range [a_l,a_r] over S, return the set I_{[a_l;a_r]} = {i |x_i \in [a_l;…
The spectral statistics of nuclei undergo through the major forms of radioactive decays ((\alpha)(\beta^-), and(\beta^+) (or EC)) and also stable nuclei are investigated. With employing the MLE technique in the nearest neighbor spacing…
Recently Sasane defined a notion of evaluating a distribution at a point using delta sequences. In this paper, we explore the relationship between generalizations of his definition and the standard definition of distributional point values.…
Motivated by the connection to a probabilistic model of phylogenetic trees introduced by Aldous, we study the recursive sequence governed by the rule $x_n = \sum_{i=1}^{n-1} \frac{1}{h_{n-1}(n-i)} x_i$ where $h_{n-1} = \sum_{j=1}^{n-1}…
This paper deals with Bayesian estimations of scale parameter of the exponential distribution based on upper record range (Rn). This has been done in two steps; point and interval. In the first step the quadratic, squared error and absolute…
We propose that supernova relic neutrino (SRN) observation can be used to set constraints on the neutrino decay models. Because of the long distance scale from cosmological supernovae to the Earth, SRN have possibility to provide much…
Forecasting the imminent catastrophic failure has a high importance for a large variety of systems from the collapse of engineering constructions, through the emergence of landslides and earthquakes, to volcanic eruptions. Failure forecast…
We give the distribution of $M_n$, the maximum of a sequence of $n$ observations from a moving average of order 1. Solutions are first given in terms of repeated integrals and then for the case where the underlying independent random…