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Rank-based Scores

Source: R/scoring_functions.R
scores.Rd

Converts a numeric vector to its rank-based scores. For uscore() (uniform scores), values become roughly equally spaced between 0 and 1, keeping their order. nscore() calculates normal scores by spacing the uniform scores along a standard normal distribution; rpscore() calculates empirical return periods by spacing the uniform scores u by 1 / (1 - u).

Usage

uscore(x, pos = "Hazen", na.rm = FALSE)

nscore(x, pos = "Hazen", na.rm = FALSE)

rpscore(x, pos = "Hazen", na.rm = FALSE)

Arguments

x

Numeric vector.

pos

Positional adjustment for uniform scores. See Details. Can be a single numeric, or could be named after one of the proponents behind a choice of the numeric: "Weibull", "Beard", "Gringorten", or "Hazen".

na.rm

Logical indicating whether NA and NaN values should be removed from the output.

Value

Vector of uniform scores corresponding to values in x.

Details

Uniform scores are calculated by (rank+a)/(n+1+2*a), where rank is the ranked x values, and a is the positional adjustment pos. Alternatively, could be named after an individual associated with a choice of a:

  • Weibull (1939) proposed a = 0.

  • Beard (1943) proposed a = -0.31.

  • Gringorten (1963) proposed a = -0.44.

  • Hazen (1914) proposed a = -0.5.

References

Beard, L. R. (1943). Statistical analysis in hydrology. Transactions of the American Society of Civil Engineers, 108, 1110–1160.

Gringorten, I. I. (1963). A plotting rule for extreme probability paper. Journal of Geophysical Research, 68(3), 813–814.

Hazen, A. (1914). Storage to be provided in impounding reservoirs for municipal water supply. Transactions of the American Society of Civil Engineers, 77, 1539–1640.

Weibull, W. (1939). A statistical theory of the strength of materials. IVB-Handl., 151.

Author

Thanks to Dr. Harry Joe for providing a starting framework for the uscore() function.

Examples

x <- c(0.3, 0.56, NA, 0.1, -12)
uscore(x)
#> [1] 0.625 0.875    NA 0.375 0.125
uscore(x, pos = "Gringorten")
#> [1] 0.6213592 0.8640777        NA 0.3786408 0.1359223
nscore(x, pos = -0.4)
#> [1]  0.3029804  1.0675705         NA -0.3029804 -1.0675705
rpscore(x)
#> [1] 2.666667 8.000000       NA 1.600000 1.142857