Related papers: Statistics of Superior Records
Statistical estimation in many contemporary settings involves the acquisition, analysis, and aggregation of datasets from multiple sources, which can have significant differences in character and in value. Due to these variations, the…
The paper concerns the optimal upper bounds on the expectations of the kth record values (k >= 1) centered about the sample mean. We consider the case, when the records are based on the infinite sequence of the independent identically…
We compute exactly the statistics of the number of records in a discrete-time random walk model on a line where the walker stays at a given position with a nonzero probability $0\leq p \leq 1$, while with the complementary probability…
We consider two independent binary i.i.d. random strings $X$ and $Y$ of equal length $n$ and the optimal alignments according to a symmetric scoring functions only. We decompose the space of scoring functions into five components. Two of…
It is known that the M\"obius function in number theory is higher order oscillating. In this paper we show that there is another kind of higher order oscillating sequences in the form $(e^{2\pi i \alpha \beta^{n}g(\beta)})_{n\in \N}$, for a…
We study the problem of comparing ageing patterns of the lifetime of k-out-of-n systems. Mathematically, this reduces to being able to decide about a stochastic ordering relationship between different order statistics. We discuss such…
A probability model exhibits instability if small changes in a data outcome result in large, and often unanticipated, changes in probability. This instability is a property of the probability model, given by a distributional form and a…
Sequence theories are an extension of theories of strings with an infinite alphabet of letters, together with a corresponding alphabet theory (e.g. linear integer arithmetic). Sequences are natural abstractions of extendable arrays, which…
Pyrosequencing is emerging as one of the important next-generation sequencing technologies. We derive the statistical distributions of this technique in terms of nucleotide probabilities of the target sequences. We give exact distributions…
This article discusses the properties of extremes of degree sequences calculated from network data. We introduce the notion of a normalized degree, in order to permit a comparison of degree sequences between networks with differing numbers…
In Nevzorov's $F^\alpha$-scheme, one deals with a sequence of independent random variables whose distribution functions are all powers of a common continuous distribution function. A key property of the $F^\alpha$-scheme is that the record…
Daily precipitation time series are composed of null entries corresponding to dry days and nonzero entries that describe the rainfall amounts on wet days. Assuming that wet days follow a Bernoulli process with success probability $p$, we…
We revisit the problem of statistical sequence matching initiated by Unnikrishnan (TIT 2015) and derive theoretical performance guarantees for sequential tests that have bounded expected stopping times. Specifically, in this problem, one is…
We investigate the probability of observing a given pattern of $n$ rises and falls in a random stationary data series. The data are modelled as a sequence of $n+1$ independent and identically distributed random numbers. This probabilistic…
We consider optimal stopping problems, in which a sequence of independent random variables is drawn from a known continuous density. The objective of such problems is to find a procedure which maximizes the expected reward; this is often…
A thermodynamic device placed outdoors, or a local ecosystem, is subject to a variety of different temperatures given by short-tem (daily) and long-term (seasonal) variations. In the long term a superstatistical description makes sense,…
A challenge in developing machine learning regression models is that it is difficult to know whether maximal performance has been reached on a particular dataset, or whether further model improvement is possible. In biology this problem is…
The problem of lossless data compression with side information available to both the encoder and the decoder is considered. The finite-blocklength fundamental limits of the best achievable performance are defined, in two different versions…
We recall some basic properties of the Beta distribution and some of its modifications. We identified around $20$ of the moment sequences of Beta distributions as important integer sequences in the OEIS base of integer sequences. Among…
Characterizations of finite sequences $\beta_{1}<\cdots<\beta_{n}$ representing expected values of order statistics from a random sample of size $n$ are given. As a by-product, a characterization of binomial mixtures, when the mixing random…