Estimation of Extreme Values by the Average Conditional Exceedance Rate Method

<table>The point estimate <svg height="20.275" id="M400" style="vertical-align:-3.56265pt" version="1.1" viewbox="0 0 38.174999 20.275" width="38.174999" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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<g transform="matrix(.012,-0,0,-.012,8.462,7.613)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g><g transform="matrix(.012,-0,0,-.012,14.174,7.613)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
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<g transform="matrix(.012,-0,0,-.012,27.575,7.613)"><path d="M478 437v-26q-39 -6 -53 -17.5t-35 -54.5q-12 -24 -26.5 -59.5l-44 -107.5l-55.5 -134q-86 -205 -103 -270q-6 -25 -32 -25q-21 0 -38.5 15t-17.5 33q0 19 25 37q40 24 75 88q18 34 31 69q7 20 -2 45q-67 191 -114 306q-17 43 -31.5 56.5t-54.5 18.5v26h202l1 -26
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</svg> of the 100-year return level based on 13 years hourly data as a function of the number <svg height="7.9499998" id="M401" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 8.6625004 7.9499998" width="8.6625004" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg> of data points above threshold. <svg height="11.225" id="M402" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 60.337502 11.225" width="60.337502" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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t96 -62.5q53 0 78 45.5t25 105.5q0 68 -35 116t-99 48z" id="x36"></path></g><g transform="matrix(.017,-0,0,-.017,37.239,10.963)"><path d="M113 -12q-24 0 -39.5 16t-15.5 42q0 24 16 40.5t40 16.5t40 -16.5t16 -40.5q0 -26 -16 -42t-41 -16z" id="x2E"></path></g><g transform="matrix(.017,-0,0,-.017,41.114,10.963)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
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</svg>m/s.</table>

Journal of Probability and Statistics

fig7

Figure 7

Figure 7: Estimation of Extreme Values by the Average Conditional Exceedance Rate Method 