The density function of product life cycles in convenience stores is found to follow the Weibull distribution. To clarify the parameters that determine these life cycles, we introduce the conditional market share—defined as the probability that a product is selected by customers only if it had been previously purchased—and the market share without any conditions. The product life cycle is more ...

The confluent hypergeometric beta distribution due to Gordy has been known since the 1990s, but not much of is in terms its mathematical properties. In this paper, we provide a comprehensive treatment properties distribution. We derive shape probability density function and expressions for cumulative function, hazard rate reversed moment generating characteristic moments, conditional entropies,...

Abstract: We investigate the probability distribution of the volatility return intervals τ for the Chinese stock market. We rescale both the probability distribution Pq(τ) and the volatility return intervals τ as Pq(τ) = 1/τf(τ/τ) to obtain a uniform scaling curve for different threshold value q. The scaling curve can be well fitted by the stretched exponential function f(x) ∼ e γ , which sugge...

We consider a bipartite quantum conductor and discuss the joint probability distribution of particle number in a subsystem and the self-information associated with the reduced density matrix of the subsystem. By extending the multi-contour Keldysh Green function technique, we calculate the Rényi entropy of a positive integer order M subjected to the particle number constraint, from which we der...

We consider estimation of the regression function in a semiparametric binary regression model defined through an appropriate link function (with emphasis on the logistic link) using likelihood-ratio based inversion. The dichotomous response variable ∆ is influenced by a set of covariates that can be partitioned as (X,Z) where Z (real valued) is the covariate of primary interest and X (vector va...

This letter characterizes the contact angle distribution based on condition that relay low earth orbit (LEO) satellite is in communication range of both ground transmitter and receiver. As one core distributions stochastic geometry-based routing analysis, analytical expression Cumulative Distribution Function (CDF) conditional derived. Furthermore, applied to analyze inaccessibility common sate...