Finance: In financial mathematics, the most popular model for a stock’s price is the lognormal distribution: if P is the stock price, then log P has a normal distribution. Suppose there are two such stock prices, P1 and P2, and that they both have a lognormal distribution. What is the probability that the sum of the prices will be greater than y? Making the simplifying assumption that the stock...

We have presented a new unified approach to model the dynamics of both the sum and difference of two correlated lognormal stochastic variables. By the Lie-Trotter operator splitting method, both the sum and difference are shown to follow a shifted lognormal stochastic process, and approximate probability distributions are determined in closed form. Illustrative numerical examples are presented ...

The problem of assessing occupational exposure using the mean or an upper percentile of a lognormal distribution is addressed. Inferential methods for constructing an upper confidence limit for an upper percentile of a lognormal distribution and for finding confidence intervals for a lognormal mean based on samples with multiple detection limits are proposed. The proposed methods are based on t...

[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 ...

The infection times of individuals in online information spread such as the inter-arrival time of Twitter messages or the propagation time of news stories on a social media site can be explained through a convolution of lognormally distributed observation and reaction times of the individual participants. Experimental measurements support the lognormal shape of the individual contributing proce...

We present a Bayesian method for estimating small area parameters under an inverse Gaussian model. The method is extended to estimate small area parameters for finite populations. The Gibbs sampler is proposed as a mechanism for implementing the Bayesian paradigm. We illustrate the method by application to household income survey data, comparing it against the usual lognormal model for positive...