Uncertainty Modelling M. H. Faber. Yovisto Academic Video Search. Extreme values, Gumbel distribution, Frechet distribution, Weibull distribution Distribution Probability Stati Functions Random Extreme Processes Continuous proce Model answered uncertainties Type Small Overview Eidgenössische Technische Hochschule Zürich (ETHZ) technology institut federal swiss ratio root squar squared when f-distribution t-distribution chi-squar typ density derived summary statistics function distribution probability technology institut federal swiss function density statistics function distribution probability technology institut federal swiss valu mean giv function density statistics function distribution probability technology institut federal swiss paramet with f-distributed said variabl distributed chi-squar betwe ratio giv variabl random when statistics function distribution probability technology institut federal swiss function density student statistics function distribution probability technology institut federal swiss giv varianc zero equal valu mean function density student statistics function distribution probability converg t-distribution larg freedom degre witn t-distributed said devided distributed normal standard giv variabl random when tudent statistics function distribution probability technology institut federal swiss technology institut federal swiss function density statistics function distribution probability technology institut federal swiss valu lean lerr giv function density statistics function distribution probability technology institut federal swiss writ then freedom degre with distributed chi-squar that assum statistics function distribution probability technology institut federal swiss degre witn said distributed chi-squar root squar giv variabl random when statistics function distribution probability technology institut federal swiss function density chi-squar statistics function distribution probability technology institut federal swiss theor limit central normal converg larg gamma complet varianc valu mean giv function density chi-squar statistics function distribution probability probability technology institut federal swiss ja-1 writ then with cas simpl consid chi-squar statistics function distribution technology institut federal swiss sum regenerativ squar that seen distributed said then variabl random independent normal standard when chi-squar statistics function distribution probability technology institut federal swiss f-distribution t-distribution chi-squar thes testing assessment used repeatedly function normal from derived which numb theory statistical classical statistics function distribution probability technology institut federal swiss updating verification paramet function distribution selection data availabl quantification statistical assessment steps fiv consist seen building model estimation overview technology institut federal swiss met being numb than short element progess met length reach that elem away element fil sort timb work exercis technology institut federal swiss ll18 model engineering developing when used information typ different building model estimation overview technology institut federal swiss model data world real 8-ii knowledg establish engine building model estimation overview federal swiss eaus heavy then equal than larg truck probability load traffic maximum annual function distribution cumulativ according that assum defined event extrem retum period return technology institut technology institut federal swiss deviation standard mean distributed said interval tim minimum then form toward tail low limited downward function density probability when weibull typ distribution valu extrem technology institut federal swiss deviation standard mean distributed said interval tim maximum then form upward zero limited downward function density probability when frechet typ distribution valu extrem increas mean constant technology institut federal swiss interval increasing said interval tim maximum then distribution gamma normal exponential exponentially function density probability tail upp when gumbel typ distribution valu extrem technology institut federal swiss sam then distribution follow independent process random ergodic period within extrem distribution valu extrem observed technology institut federal swiss distribution valu extrem 5-year annual monthly technology institut federal swiss cov concret thickness chain link weak soil pesticid unit area volum quantity certain larg small interested could distribution valu extrem technology iur federal swiss year rainfall season wint wav high year earthquak interval tim quantity certain larg small valu interested oft engineering distribution valu extrem technology institut federal swiss year mak typhoon that probability what which averag process poisson follow typhoon occurrenc region exercis technology institut federal swiss year mak typhoon that probability what which averag process poisson follow landfall typhoon occurrenc region exercis technology institut federal swiss period long period referenc short event extrem model extrapolat application engineering useful very oft regard assumption first weakly realization basis determined moment addition stationary ergodic strictly said process ergodicity stationarity process random technology institut federal swiss auto-correlation function valu mean first weakly tim shift invariant moment stationary strictly said process ergodicity stationarity process random technology institut federal swiss distribution probability joint said process gauss normal process random technology institut federal swiss defined function coefficient correlation auto-covarianc function covarianc component mor with process valued vector process random continuous technology institut federal swiss deviation standard till covarianc becom defined function auto-covarianc continuous process random technology institut federal swiss process valued scalar ref auto-correlation giv point betwe correlation tim function jack realization possibl valu mean continuous process random technology institut federal swiss deviation standard covarianc becom defined function auto-covarianc continuous process random technology institut federal swiss process valued scalar ref auto-correlation giv point betwe correlation tim function ocess realization possibl valu mean process random continuous institut federal fall rain speed wind wat variation spac sampl belong realization tim over continuously which process continuous process random technology technology institut federal swiss technology institut federal swiss making decision influenc uncertainti answered technology institut federal swiss making decision influenc uncertainti tang mini azur answered technology institut federal swiss making decision influenc uncertainti answered technology institut federal swiss interval varianc averag characteristics statistical descriptor sampl estimator statistics function distribution probability building model estimation overview process random extrem tim last from with catching assessment classroom result presentation lectur today content qvim mjae technology institut federal swiss confidenc varianc averag characteristics statistical descriptor sampl estimator statistics function distribution probability building model estimation overview extrem process random continuous tim last from with catching assessment classroom result presentation lectur today content making decision influenc uncertainti answered technology institut federal swiss switzerland zurich technology institut federal swiss fab michael prof engineering environmental surveying civil theory probability statistics