Mean-shift outliers model in skew scale-mixtures of normal distributions

Parameter estimation of three-parameter Weibull probability model based on outlier detection

“…The probability in the ith subinterval is denoted as p i . The cumulative probability density of the ith subinterval is summed from p 1 to p i , as shown in formula (9). The probability density of the ith subinterval is the difference of p i with respect to x i , as shown in formula (10).…”

“…6 In addition to the Weibull model, two other statistical distributions have been used to describe the material data: the normal distribution and the lognormal distribution. [7][8][9] Comparatively, the two-parameter Weibull distribution is mostly used because: (a) it is more accurate in describing glass strength data than the normal distribution, 2 and (b) it is always more conservative in the tail of the distribution than the lognormal distribution. 3 Conservative estimates are preferred for engineering design applications considering the safety margin.…”