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scipy.stats.mstats.plotting_positions

scipy.stats.mstats.plotting_positions(data, alpha=0.4, beta=0.4)

Returns plotting positions (or empirical percentile points) for the data.

Plotting positions are defined as (i-alpha)/(n+1-alpha-beta), where:

• i is the rank order statistics
• n is the number of unmasked values along the given axis
• alpha and beta are two parameters.

Typical values for alpha and beta are:

• (0,1) : p(k) = k/n, linear interpolation of cdf (R, type 4)

• (.5,.5) : p(k) = (k-1/2.)/n, piecewise linear function

  (R, type 5)

• (0,0) : p(k) = k/(n+1), Weibull (R type 6)

• (1,1) : p(k) = (k-1)/(n-1), in this case,

  p(k) = mode[F(x[k])]. That’s R default (R type 7)

• (1/3,1/3): p(k) = (k-1/3)/(n+1/3), then

  p(k) ~ median[F(x[k])].

  The resulting quantile estimates are approximately median-unbiased regardless of the distribution of x. (R type 8)

• (3/8,3/8): p(k) = (k-3/8)/(n+1/4), Blom. The resulting quantile estimates are approximately unbiased if x is normally distributed (R type 9)

• (.4,.4) : approximately quantile unbiased (Cunnane)

• (.35,.35): APL, used with PWM

• (.3175, .3175): used in scipy.stats.probplot

Parameters :

data : array_like

Input data, as a sequence or array of dimension at most 2.

alpha : float, optional

Plotting positions parameter. Default is 0.4.

beta : float, optional

Plotting positions parameter. Default is 0.4.

Returns :

positions : MaskedArray

The calculated plotting positions.