While lognormal distributions have demonstrated great utility in a number of applications related to decision sciences, practitioners find few – if any – tables of its cumulative distribution function available to support their work. This paper describes a “standardized” form of the lognormal distribution and a methodology by which tables of its cumulative distribution function can be generated...

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...

Generalized linear models might not be appropriate when the probability of extreme events is higher than that implied by the normal distribution. Extending the method for estimating the parameters of a double Pareto lognormal distribution (DPLN) in Reed and Jorgensen (2004), we develop an EM algorithm for the heavy-tailed Double-Pareto-lognormal generalized linear model. The DPLN distribution i...

[1] We use four-year time series of precipitable water (PW) and zenith neutral delay (ZND) derived from a GPS network in Hawaii to show that the statistical distributions of these quantities are closely approximated by the lognormal distribution. The long term average and median values of precipitable water decline exponentially with height, or very nearly so. The arithmetic standard deviation ...

Because the future price of a stock at time t cannot be predicted with certainty, we model it as a random variable, denoted here by S(t). Since random variables are characterised by their distribution functions it is useful to have a notation to express this concept. Definition 1.1 We use the symbol X D = Y to mean that the random variables X and Y have the same distribution,i.e., P (X ≤ t) = P...

The subgrid-scale representation of hydrometeor fields is important for calculating microphysical process rates. In order to represent subgrid-scale variability, the Cloud Layers Unified By Binormals (CLUBB) parameterization uses a multivariate probability density function (PDF). In addition to vertical velocity, temperature, and moisture fields, the PDF includes hydrometeor fields. Previously,...