This paper deals with the estimation of the lognormal-Pareto and the lognormal-Generalized Pareto distributions, for which a general result concerning asymptotic optimality of maximum likelihood estimation cannot be proved. We develop a method based on probability weighted moments, showing that it can be applied straightforwardly to the first distribution only. In the lognormal-Generalized Pare...

In this paper we apply the idea of the WKB method to derive an effective single lognormal approximation for the probability distribution of the sum of two correlated lognormal variables. An approximate probability distribution of the sum is determined in closed form, and illustrative numerical examples are presented to demonstrate the validity and accuracy of the approximate distribution. Our a...

Performance of computers is usually measured by using benchmark suites. There has been a long debate among computer architects on how to aggregate the individual program results to present a summary of performance over the entire suite. Many researchers have criticised the use of Geometric Mean (GM) but SPEC continues to use it to report performance. Mashey [7] has strongly supported the use of...

The physical meaning of the composite Nakagami-lognormal fading model is not well understood by many researchers using the model. The signal power transfer and transform at the interface between the global lognormal shadowing sub-channels and the local Nakagami multipath sub-channels in the presence of correlation between these diversity sub-channels is rather complex. This is the main reason w...

The development of an ultra high energy air shower has an intrinsic energy fluctuation due both to the first interaction point and to the cascade development. Here we show that for a given primary energy this air shower energy fluctuation has a lognormal distribution and thus observations will estimate that primary energy with a lognormal error distribution. We analyze the UHECR energy spectrum...

Multiple single antenna terminals transmit simultaneously to an array of hundreds of antennas in the uplink of a multi-user massive multiple-inputmultiple-output (MIMO) system. Under Rayleigh fading and lognormal shadowing, the expression for the probability density function (PDF) for signal-to-interference-plus-noise-ratio (SINR) does not exist in a closed-form, which is required to calculate ...

We analyze the distribution of computational eeort required by backtracking algorithms on unsatissable CSPs, using analogies with reliability models, where lifetime of a specimen before failure corresponds to the runtime of backtracking on unsatissable CSPs. We extend the results of 7] by showing empirically that the lognormal distribution is a good approximation of the backtracking eeort on un...