### Statistics Seminar: STA 290

Thursday, May 31st, 2012 at 4:10pm, MSB 1147 (Colloquium Room)

Refreshments at 3:30pm prior to seminar in MSB 4110 (Statistics Lounge)

Speaker: **Anna Panorska** (University of Nevada, Reno)

Title: **Trivariate Models for Stochastic Episodes with Applications to Hydrology, Climate and Finance**

Abstract: We consider the problem of modeling the joint distribution of the duration, maximum and magnitude of stochastic episodes (events). An event is defined as consecutive observations of a process above (or below) a threshold. Examples of events include growth (or decline) periods of a financial series or climatic or hydrologic episodes, e.g. flood, draught, heat wave, cold spell, etc. Let N, X, and Y describe episodes as their duration (N), magnitude (X) and maximum/peak (Y). The distribution of the vector (N, X, Y) is of direct interest to water management, energy management companies, disaster management, health departments as well as state and federal regulatory agencies. In particular, the probability of extreme events associated with large values of (N, X, Y) are of primary interest. We present the exact joint distribution of the vector (N, X, Y) and its marginals and conditionals, when N has a geometric distribution, X is the random sum and Y is the random maximum of N iid exponential random variables. We illustrate the modeling potential of these distributions using hydroclimatic data.