SMp(x) Distribution Calculator

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The smallest value the variable x can take. SMp(x) = 0 for any x below this value.
The largest value the variable x can take. SMp(x) = 0 for any x above this value.
The value of x where SMp(x) reaches its peak. Must lie strictly between PXmin and Xmax.
Controls the curvature of the left side (PXmin to ML). p1 = 1 gives a linear rise; p1 > 1 gives a concave rise; 0 < p1 < 1 gives a convex rise.
Controls the curvature of the right side (ML to Xmax). p2 = 1 gives a linear fall; p2 > 1 gives a concave fall; 0 < p2 < 1 gives a convex fall.
The point at which to evaluate the density and cumulative probability.
Choose which tail or interval probability to compute.
SMp(x) density at xCentral region
0.173611

Value of the probability density function at the specified x

P(X <= x) - cumulative probability0.289352
Interval / tail probability0.289352
Max (normalized peak)0.25
Mean5.9167
Variance3.126389
Standard deviation1.7682
0.17361156.9% below · x

Density at x = 5 is 0.173611; P(X <= 5) = 28.94%.

  • 28.9% of the probability mass falls at or below x = 5.
  • The distribution has mean 5.9167 and standard deviation 1.7682.
  • p1 (2) > p2 (1): the left side rises more steeply than the right falls, producing a left-skewed shape.
  • The normalized peak density is 0.2500 at mode ML = 6.

Next stepAdjust p1 and p2 to match your data shape: equal powers create a symmetric distribution, unequal powers create skew. To reproduce a uniform distribution set p1 = p2 = 1 with ML at the midpoint.

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