The Weibull modulus is a shape parameter for the Weibull distribution model which, in this case, maps the probability of failure of a component at varying stresses.
42.
The shape parameter is 1 for sphere and 3 / 2 for a very long wire, indicating that melting-point depression is suppressed in nanowires compared to nanoparticles.
43.
In such a plot, the shape parameter estimators \ hat { \ alpha }, \ hat { \ beta } correspond to the maxima of the likelihood function.
44.
\alpha, which must be greater than 0 and less than or equal to 2, is the shape parameter or index of stability, which determines how heavy the tails are.
45.
These include the Burr Type XII distribution ( also known as the " Singh-Maddala distribution " ) and the Dagum distribution, both of which include a second shape parameter.
46.
The Pareto Type I distribution is characterized by a scale parameter " x " m and a shape parameter ?, which is known as the " tail index ".
47.
However, the resulting shape parameters have been found to lie in the range leading to undefined means and variances, which underlines the fact that reliable data analysis is often impossible.
48.
Misner defines parameters \ Omega ( t ) and R ( t ) which measure the volume of spatial slices, as well as " shape parameters " \ beta _ k, by
49.
The Holtsmark distribution is a special case of a stable distribution with the index of stability or shape parameter \ alpha equal to 3 / 2 and skewness parameter \ beta of zero.
50.
Misner showed that the shape parameters \ beta _ \ pm ( t ) act like the coordinates of a point mass moving in a triangular potential with steeply rising walls with friction.
