Related papers: Notes on the sum and maximum of independent expone…
Let $x_{i,j}$, $1 \le i \le m$, $1 \le j \le n_i$, be observations from a doubly-indexed sequence $\{X_{i,j}\}$ of independent random variables (all of them discrete, or all of them absolutely continuous). Suppose that each $X_{i,j}$ has…
We derive the exact probability density function of the product of $N$ independent variance-gamma random variables with zero location parameter. We then apply this formula to derive formulas for the cumulative distribution function and…
Let $\{\xi_1,\xi_2,\ldots\}$ be a sequence of independent random variables, and $\eta$ be a counting random variable independent of this sequence. In addition, let $S_0:=0$ and $S_n:=\xi_1+\xi_2+\cdots+\xi_n$ for $n\geqslant1$. We consider…
We characterize the exponential distribution in terms of the regression of a record value with non-adjacent record values as covariates. We also study characterizations based on the regression of linear combinations of record values.
The formula for probability density functions (PDFs) has been extended to include PDF for energy dissipation rates in addition to other PDFs such as for velocity fluctuations, velocity derivatives, fluid particle accelerations, energy…
The sum of correlated gamma random variables appears in the analysis of many wireless communications systems, e.g. in systems under Nakagami-m fading. In this Letter we obtain exact expressions for the probability density function (PDF) and…
Density estimation plays a crucial role in many data analysis tasks, as it infers a continuous probability density function (PDF) from discrete samples. Thus, it is used in tasks as diverse as analyzing population data, spatial locations in…
In this paper I describe two general methods of constructing a probability density function (pdf) of a Benford random variable, and show that the pdf of every Benford random variable may be constructed by these methods. These constructions…
Dispersion of a passive scalar from concentrated sources in fully developed turbulent channel flow is studied with the probability density function (PDF) method. The joint PDF of velocity, turbulent frequency and scalar concentration is…
The normalized probability density function (PDF) of global measures of a large class of highly correlated systems has previously been demonstrated to fall on a single non-Gaussian "universal" curve. We derive the functional form of the…
Let $X$ be an arbitrary real-valued random variable (r.v.), with the characteristic function (c.f.) $f$. Integral expressions for the c.f.\ of the r.v.'s $\max(0,X)$ in terms of $f$ are given, as well as other related results. Applications…
The spectrum profile that emerges in molecular spectroscopy and atmospheric radiative transfer as the combined effect of Doppler and pressure broadenings is known as the Voigt profile function. Because of its convolution integral…
In this paper, we study the statistical evolution of the large-scale structure (LSS), focusing on the joint probability distribution function (PDF) of the coarse-grained cosmic field and its role in constructing effective dynamics. As the…
The probability distribution function (PDF) of the mass surface density is an essential characteristic of the structure of molecular clouds or the interstellar medium in general. Observations of the PDF of molecular clouds indicate a…
Multivariate extreme value statistical analysis is concerned with observations on several variables which are thought to possess some degree of tail-dependence. In areas such as the modeling of financial and insurance risks, or as the…
We study scaling properties of stochastic aggregation processes in one dimension. Numerical simulations for both diffusive and ballistic transport show that the mass distribution is characterized by two independent nontrivial exponents…
We revisit the problem of condensation for independent, identically distributed random variables with a power-law tail, conditioned by the value of their sum. For large values of the sum, and for a large number of summands, a condensation…
We consider the discrete three dimensional scan statistics. Viewed as the maximum of an 1-dependent stationary r.v.'s sequence, we provide approximations and error bounds for the probability distribution of the three dimensional scan…
The general relationship between an arbitrary frequency distribution and the expectation value of the frequency distributions of its samples is discussed. A wide set of measurable quantities ("invariant moments") whose expectation value…
A natural problem in the context of the coupon collector's problem is the behavior of the maximum of independent geometrically distributed random variables (with distinct parameters). This question has been addressed by Brennan et al.…