Related papers: On the Distribution of the Sum of n Non-Identicall…
In probability theory, there is a tendency to treat one random variable with a given distribution as being just as good as any other. By and large this is fine because probability is (mostly) concerned with distributional properties of…
In this paper, we analyze the set of all possible aggregate distributions of the sum of standard uniform random variables, a simply stated yet challenging problem in the literature of distributions with given margins. Our main results are…
It is proved that the sum of n independent but non-identically distributed doubly truncated Normal distributions converges in distribution to a Normal distribution. It is also shown how the result can be applied in estimating a constrained…
A theoretical framework is developed to describe the transformation that distributes probability density functions uniformly over space. In one dimension, the cumulative distribution can be used, but does not generalize to higher…
In this work, we revisit the problem of uniformity testing of discrete probability distributions. A fundamental problem in distribution testing, testing uniformity over a known domain has been addressed over a significant line of works, and…
In this letter, we give a concise, closed-form expression for the differential entropy of the sum of two independent, non-identically-distributed exponential random variables. The derivation is straightforward, but such a concise entropy…
Exact formulas are derived for the probability density functions of the sum and difference of two independent non-central gamma distributed random variables, with both series and integral representations of the density presented. These…
The distribution function of the sum of i.i.d. random variables of the special form is considered. Such sum describes messages posterior probabilities for random coding in binary symmetric channel. Close non-asymptotic lower and upper…
We consider the distribution of the sum and the maximum of a collection of independent exponentially distributed random variables. The focus is laid on the explicit form of the density functions (pdf) of non-i.i.d. sequences. Those are…
The distribution of the sum of r-th power of standard normal random variables is a generalization of the chi-squared distribution. In this paper, we represent the probability density function of the random variable by an one-dimensional…
We consider the problem of computing the joint distribution of order statistics of stochastically independent random variables in one- and two-group models. While recursive formulas for evaluating the joint cumulative distribution function…
Some properties of the inverse of the Normal distribution are studied. Its derivatives, integrals and asymptotic behavior are presented.
We present an analytic method for computing the moments of a sum of independent and identically distributed random variables. The limiting behavior of these sums is very important to statistical theory, and the moment expressions that we…
In this paper, the joint distribution of the sum and maximum of independent, not necessarily identically distributed, nonnegative random variables is studied for two cases: i) continuous and ii) discrete random variables. First, a recursive…
Linear combinations of independent random variables have been extensively studied in the literature. However, most of the work is based on some specific distribution assumptions. In this paper, a companion of (J. Appl. Probab. 48 (2011)…
For a sample of absolutely bounded i.i.d. random variables with a continuous density the cumulative distribution function of the sample variance is represented by a univariate integral over a Fourier series. If the density is a polynomial…
We prove that the distribution of the product of two correlated normal random variables with arbitrary means and arbitrary variances is infinitely divisible. We also obtain exact formulas for the probability density function of the sum of…
We study the learnability of sums of independent integer random variables given a bound on the size of the union of their supports. For $\mathcal{A} \subset \mathbf{Z}_{+}$, a sum of independent random variables with collective support…
We are concerned with the general problem of proving the existence of joint distributions of two discrete random variables $M$ and $N$ subject to infinitely many constraints of the form $\mathbb{P}\left(M=i,N=j\right)=0$. In particular, the…
The (general) hypoexponential distribution is the distribution of a sum of independent exponential random variables. We consider the particular case when the involved exponential variables have distinct rate parameters. We prove that the…