# Probability Weighted Moments: Definition and Relation to Parameters of Several Distributions Expressable in Inverse Form

##### Citations

^{1}

2,668 citations

### Cites background from "Probability Weighted Moments: Defin..."

...Probability Weighted Moments Greenwood et al. (1979) defined probability weighted moments (PWMs) to be the quantities...

[...]

1,275 citations

### Cites background from "Probability Weighted Moments: Defin..."

...Greenwood et al. (1979) generally favored the latter approach, but here we will consider the moments fl, = M t,,,o = ECX{F(X))‘I (I = 0, L2, ....

[...]

...Probability-weighted moments, a generalization of the usual moments of a probability distribution, were introduced by Greenwood et al. (1979)....

[...]

^{1}

1,233 citations

### Cites background or methods from "Probability Weighted Moments: Defin..."

...Greenwood et al. (1979) exhibited several distributions for which the relationship between the parameters of the distribution and the PWM's M, r, s is simpler than the relationship between the parameters and the conventional moments Mp, o....

[...]

...Property 3 of Section 1 implies a close connection between generalized Pareto and GEV distributions with equal values for their shape parameters, and, as Hosking, Wallis, and Wood (1985) remarked, applications of the GEV distributions, particularly in hydrology, usually involve the case - 2 < k < 1....

[...]

...Greenwood et al. (1979) exhibited several distributions for which the relationship between the parameters of the distribution and the PWM's M, r, s is simpler than the relationship between the parameters and the conventional moments Mp, o. Hosking et al. (1985) showed that efficient estimators of parameters and quantiles of the GEV distribution can be obtained using PWM's....

[...]

...Greenwood et al. (1979) exhibited several distributions for which the relationship between the parameters of the distribution and the PWM’s MI,.,. is simpler than the relationship between the parameters and the conventional moments M ~, 0,0, Hosking et al. (1985) showed that efficient estimators of…...

[...]

...Greenwood et al. (1979) exhibited several distributions for which the relationship between the parameters of the distribution and the PWM's M, r, s is simpler than the relationship between the parameters and the conventional moments Mp, o. Hosking et al. (1985) showed that efficient estimators of parameters and quantiles of the GEV distribution can be obtained using PWM's. Hosking (1986) gave a general exposition of the theory of PWM's....

[...]

865 citations

742 citations

### Cites methods from "Probability Weighted Moments: Defin..."

...For example, for the Gumbel and Weibull distributions [15], we have...

[...]

##### References

1,569 citations

430 citations

185 citations

134 citations

127 citations