Related papers: On Probabilistic Proofs of Certain Binomial Identi…

In this work, we give a novel general approach for distribution testing. We describe two techniques: our first technique gives sample-optimal testers, while our second technique gives matching sample lower bounds. As a consequence, we…

A product difference equation is proved and used for derivation by elementary methods of four combinatorial identities, eight combinatorial identities involving generalized harmonic numbers and eight combinatorial identities involving…

Using an elementary approach involving the Euler Beta function and the binomial theorem, we derive two polynomial identities; one of which is a generalization of a known polynomial identity. Two well-known combinatorial identities, namely…

The aim of this paper is to show a possibility to identify multivariate distribution by means of specially constructed one-dimensional random variable. We give some inequalities which may appear to helpful for a construction of multivariate…

Using sequences of finite length with positive integer elements and the inversion statistic on such sequences, a collection of binomial and multinomial identities are extended to their $q$-analog form via combinatorial proofs. Using the…

We first establish the result that the Narayana polynomials can be represented as the integrals of the Legendre polynomials. Then we represent the Catalan numbers in terms of the Narayana polynomials by three different identities. We give…

Let $LA_{n}(\tau)$ be the length of the longest alternating subsequence of a uniform random permutation $\tau\in[n]$. Classical probabilistic arguments are used to rederive the asymptotic mean, variance and limiting law of $LA_{n}(\tau)$.…

In this article, the exponentiated discrete Lindley distribution is presented and studied. Some important distributional properties are discussed. Using the maximum likelihood method, estimation of the model parameters is investigated.…

We lift to the multivariate Eulerian polynomials the identity implying that univariate Eulerian polynomials are palindromic. As a consequence of this generalization, we obtain nice combinatorial identities that can be directly extracted…

The problem of testing mutually exclusive hypotheses with dependent test statistics is considered. Bayesian and frequentist approaches to multiplicity control are studied and compared to help gain understanding as to the effect of test…

Nonprobability (convenience) samples are increasingly sought to reduce the estimation variance for one or more population variables of interest that are estimated using a randomized survey (reference) sample by increasing the effective…

Binomial distributions capture the probabilities of `heads' outcomes when a (biased) coin is tossed multiple times. The coin may be identified with a distribution on the two-element set {0,1}, where the 1 outcome corresponds to `head'. One…

We provide a lower bound on the probability that a binomial random variable is exceeding its mean. Our proof employs estimates on the mean absolute deviation and the tail conditional expectation of binomial random variables.

We present novel bounds for estimating discrete probability distributions under the $\ell_\infty$ norm. These are nearly optimal in various precise senses, including a kind of instance-optimality. Our data-dependent convergence guarantees…

Let a deck of n cards be shuffled by successively exchanging the cards in positions 1, 2, ..., n with cards in randomly chosen positions. We show that for n equal to 18 or greater, the identity permutation is the most likely. We prove a…

A composite likelihood is an inference function derived by multiplying a set of likelihood components. This approach provides a flexible framework for drawing inference when the likelihood function of a statistical model is computationally…

We first review existing sequential methods for estimating a binomial proportion. Afterward, we propose a new family of group sequential sampling schemes for estimating a binomial proportion with prescribed margin of error and confidence…

A method of calculating probability values from a system of marginal constraints is presented. Previous systems for finding the probability of a single attribute have either made an independence assumption concerning the evidence or have…

A collection of $n$ random events is said to be $(n - 1)$-wise independent if any $n - 1$ events among them are mutually independent. We characterise all probability measures with respect to which $n$ random events are $(n - 1)$-wise…

We initiate the study of differentially private hypothesis testing in the local-model, under both the standard (symmetric) randomized-response mechanism (Warner, 1965, Kasiviswanathan et al, 2008) and the newer (non-symmetric) mechanisms…