In a Weibull distribution, which of the following describes the shape parameter?

The correct answer is A. The skewness and kurtosis of the distribution . In the CSSBB material, the Weibull shape parameter is identified as β , and the text states that the shape parameter is what gives the Weibull distribution its flexibility . By changing β, the distribution can model a wide variety of data patterns. For example, when β = 1 , the Weibull becomes the exponential distribution; when β = 2 , it becomes the Rayleigh distribution; and when β is between about 3 and 4 , it approximates the normal distribution.

This means the shape parameter controls the form of the distribution, including how skewed it is and how the curve behaves. By contrast, the scale parameter determines the range or spread on the x-axis, and the location parameter defines a failure-free zone or shift along the x-axis. Therefore, among the listed choices, the best description of the shape parameter is the one tied to the distribution’s shape characteristics, namely skewness and kurtosis , rather than scale, intercept, or mean.