Related papers: On the Sum of Extended $\eta$-$\mu$ Variates with …
The probability density function (PDF) and cumulative distribution function of the sum of L independent but not necessarily identically distributed squared \eta-\mu variates, applicable to the output statistics of maximal ratio combining…
In this paper, we derive closed-form exact expressions for the main statistics of the ratio of squared alpha-mu random variables, which are of interest in many scenarios for future wireless networks where generalized distributions are more…
The analysis of systems operating in future frequency ranges calls for a proper statistical channel characterization through generalized fading models. In this paper, we adopt the Extended $\eta$-$\mu$ and $\kappa$-$\mu$ models to…
The XGamma distribution is a generated distribution from a mixture of Exponential and Gamma distributions. It is found that in many cases the XGamma has more flexibility than the Exponential distribution. In this paper we consider the sum…
In this work, the product of two independent and non-identically distributed (i.n.i.d) $\kappa - \mu $ shadowed random variables is studied. We derive the series expression for the probability density function (PDF), cumulative distribution…
In this paper, a very accurate approximation method for the statistics of the sum of M\'{a}laga-$\mathcal{M}$ random variates with pointing error (MRVs) is proposed. In particular, the probability density function of MRV is approximated by…
Approximate outage probability expressions are derived for systems employing maximum ratio combining, when both the desired signal and the interfering signals are subjected to $\eta-\mu$ fading, with the interferers having unequal power.…
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…
This paper re-examines the density for sums of independent exponential, Erlang and gamma random variables. By using a divided difference perspective, the paper provides a unified approach to finding closed-form formulae for such…
The probability density function (PDF) and cumulative distribution function of the sum of L independent but not necessarily identically distributed Gamma variates, applicable to the output statistics of maximal ratio combining (MRC)…
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 of the sum of independent identically distributed uniform random variables is well-known. However, it is sometimes necessary to analyze data which have been drawn from different uniform distributions. By inverting the…
The distribution of the sum of dependent risks is a crucial aspect in actuarial sciences, risk management and in many branches of applied probability. In this paper, we obtain analytic expressions for the probability density function (pdf)…
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…
Capitalizing on the recently proposed Fisher-Snedecor F composite fading model, in this letter, we investigate the sum of independent but not identically distributed (i.n.i.d.) Fisher-Snedecor F variates. First, a novel closed-form…
Let $\{\xi_1,\xi_2,\ldots\}$ be a sequence of independent random variables (not necessarily identically distributed), and $\eta$ be a counting random variable independent of this sequence. We obtain sufficient conditions on…
This paper proposes a comprehensive and unprecedented framework that streamlines the derivation of exact, compact -- yet tractable -- solutions for the probability density function (PDF) and cumulative distribution function (CDF) of the sum…
Let $\{\xi_1,\xi_2,\ldots\}$ be a sequence of independent random variables, and $\eta$ be a counting random variable independent of this sequence. We consider conditions for $\{\xi_1,\xi_2,\ldots\}$ and $\eta$ under which the distribution…
In this paper we discuss a closed-form approximation of the likelihood functions of an arbitrary diffusion process. The approximation is based on an exponential ansatz of the transition probability for a finite time step $\Delta t$, and a…
The statistical characterization of the sum of random variables (RVs) are useful for investigating the performance of wireless communication systems. We derive exact closed-form expressions for the probability density function (PDF) and…