Probability density function

About: Probability density function is a research topic. Over the lifetime, 22321 publications have been published within this topic receiving 422885 citations. The topic is also known as: probability function & PDF.

On the performance analysis of equal-gain diversity receivers over generalized gamma fading channels

Abstract: A versatile envelope distribution which generalizes many commonly used models for multipath and shadow fading is the so-called generalized Gamma (GG) distribution. By considering the product of N GG random variables (RV)s, novel expressions for its moments-generating, probability density, and cumulative distribution functions are obtained in closed form. These expressions are used to derive a closed-form union upper bound for the distribution of the sum of GG distributed RVs. The proposed bound turns out to be an extremely convenient analytical tool for studying the performance of TV-branch equal-gain combining receivers operating over GG fading channels. For such receivers, first the moments of the signal-to-noise (SNR) at the output, including average SNR and amount of fading, are obtained in closed form. Furthermore, novel union upper bounds for the outage and the average bit error probability are derived and evaluated in terms of Meijer's G-functions. The tightness of the proposed bounds is verified by performing comparisons between numerical evaluation and computer simulations results

Optimizing and satisficing in stochastic cost‐volume‐profit analysis

Abstract: This paper examines some of the implications of introducing penalties for output not equalling demand by employing a general stochastic model for a firm facing an uncertain demand with a known probability density function. Several alternative objectives of the firm are considered: (1) maximization of expected profits; (2) maximization of the probability of achieving a particular target level of profits; and (3) maximization of target profits, given a target level of the probability of their being achieved. It is shown that the resulting probability density function of profits is not well defined. The shape and location of the function depend on the relative magnitudes of the model parameters and the output decision. Several important implications of this result for cost-volume-profit analysis are discussed.

A first step towards a direct inversion of the Lyman forest in QSO spectra

Abstract: A method for the recovery of the real space line-of-sight mass density field from Lyman absorption in QSO spectra is presented. The method makes use of a Lucy-type algorithm for the recovery of the HI density. The matter density is inferred from the HI density assuming that the absorption results from a photoionized intergalactic medium that traces the mass distribution as suggested by recent numerical simulations. Redshift distortions are corrected iteratively from a simultaneous estimate of the peculiar velocity. The method is tested with mock spectra obtained from N-body simulations. The density field is recovered reasonably well up to densities where the absorption features become strongly saturated. The method is an excellent tool with which to study the density probability distribution and clustering properties of the mass density in the (mildly) non-linear regime. Combined with redshift surveys along QSO sightlines, the method will make it possible to relate the clustering of high-redshift galaxies to the clustering of the underlying mass density. We further show that accurate estimates for (Ωbarh2)2J-1H(z)-1 and higher order moments of the density probability function can be obtained despite the missing high-density tail of the density distribution if a parametric form for the probability distribution of the mass density is assumed.

Defining Triangular Probability Distributions from Historical Cost Data

Abstract: During the development of an automated cost estimating system, several factors led to the selection of the triangular probability-density function to model historical construction costs. The triangular-density function is customarily used when function parameters are directly estimated by experts. A typical example is for estimating activity durations by identifying a minimum value, a most likely value, and a maximum value. These values are then used to construct triangular-density functions to represent uncertain activity durations. For this work, however, it was necessary to estimate parameters of the triangular-density function using historical cost data. A methodology was developed to generate test data and compare three methods of parameter estimation—maximum likelihood, moment matching, and least-squares curve-fitting techniques. It is concluded that optimized moment matching and least-squares techniques produce more accurate parameter estimates, while maximum likelihood estimation yields less accurate results. It is further concluded that the least-squares minimization method always performed as well as or better than the optimized moment matching technique and was therefore selected as the method of choice for the project.