Statistical Prediction of Maximum Time-Variant Inlet Distortion Levels

Abstract

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Analyzing Extreme Disturbance Events: Fire in Los Padres National Forest

“…Fisher and Tippet (1928) first described the asymptotic theory of extreme value distributions, although the flood analysis of Gumbel (1958) is the most prominent early work on the statistics of extremes. Later authors derived generalized forms of extreme value distributions (e.g., Maritz andMunro 1967, Jacocks andKneile 1975). The statistics of extremes have been applied to a wide variety of problems, and there are now current texts on applied (e.g., Kinnison 1985) and theoretical aspects (e.g., Leadbetter et al 1983, Galambos 1987.…”

“…A brief description of the statistics of extremes is given here, and the reader should consult the references for a more complete development. Notation will be similar to that used in Jacocks and Kneile (1975) and Gaines and Denny (1993). This approach examines statistical properties of observations that are extreme in comparison to the rest of the same population.…”

“…Three asymptotic families of distributions have been found Tippet 1928, Gumbel 1958) that characterize the extremal distributions of a variety of parent distributions. All three asymptotic families can be represented as a single generalized cumulative distribution, whose shape is determined by three parameters, ␣, ␤, and (Jacocks and Kneile 1975); here x still refers to event magnitude, i.e.,…”

“…Other interpretations are possible for parameters, depending on the family. Modal event magnitude is ; ␣ measures how quickly F(x) rises with the natural logarithm of time; and ␣/␤ estimates the limiting magnitude observable (Jacocks and Kneile 1975).…”

Improved statistical analysis method for prediction of maximum inletdistortion

“…Figures 6,7, arc £ compare the predicled and measured peak distortion maps lor three lpvels of average turbulence. For all three defined as they are not a part of the input to the statistical prediction method.…”