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The Uniform Distribution

Source: R/api-distributions.R
nv_uniform.Rd

Density (nv_dunif), distribution function (nv_punif), and quantile function (nv_qunif) for the Uniform distribution on the interval from min to max.

Usage

nv_dunif(x, min = 0, max = 1, log = FALSE)

nv_punif(q, min = 0, max = 1, lower_tail = TRUE, log_p = FALSE)

nv_qunif(p, min = 0, max = 1, lower_tail = TRUE, log_p = FALSE)

Arguments

x, q

(arrayish)
Quantiles at which to evaluate the density (x) or the distribution function (q).

min, max

(arrayish)
Lower and upper limits of the distribution. Either scalars, or arrays of exactly the same shape as x/q/p, in which case the interval varies elementwise and each element of x/q/p is evaluated against its own min/max.

log, log_p

(logical(1))
If TRUE, the densities/probabilities are given as logarithms. For nv_qunif this describes the input p.

lower_tail

(logical(1))
If TRUE (default), probabilities are \(P(X \le x)\); otherwise, \(P(X > x)\).

p

(arrayish)
Probabilities at which to evaluate the quantile function. Values outside \([0, 1]\) give NaN.

Value

nv_dunif(), nv_punif(), and nv_qunif() return an arrayish with the same shape and data type as x/q/p.

Details

The Uniform distribution has probability density function: $$f(x) = \frac{1}{b - a}, \quad a \le x \le b$$ and zero elsewhere, where \(a\) is min and \(b\) is max. The min and max are converted to the data type of x/q/p.

All three are univariate functions evaluated elementwise, returning one value per element of x/q/p. Non-scalar min/max therefore give a separate univariate Uniform per element, not a multivariate Uniform over the hyper-rectangle \(\prod_i [a_i, b_i]\). For that, reduce over the result: nv_reduce_prod(nv_dunif(x, min, max)), or nv_reduce_sum(nv_dunif(x, min, max, log = TRUE)) on the log scale.

See also

nv_runif() for sampling from a uniform distribution.

Examples

x <- nv_array(c(-0.5, 0, 0.25, 1, 1.5))
nv_dunif(x)
#> AnvlArray
#>  0
#>  1
#>  1
#>  1
#>  0
#> [ CPUf32{5} ] 
nv_dunif(x, min = -1, max = 2)
#> AnvlArray
#>  0.3333
#>  0.3333
#>  0.3333
#>  0.3333
#>  0.3333
#> [ CPUf32{5} ] 
nv_dunif(x, log = TRUE)
#> AnvlArray
#>  -inf
#>     0
#>     0
#>     0
#>  -inf
#> [ CPUf32{5} ] 

# `min`/`max` may vary elementwise, giving one univariate Uniform per
# element rather than a single distribution over a hyper-rectangle
lower <- nv_array(c(-1, -1, 0, 0, 1))
upper <- nv_array(c(0, 1, 1, 2, 2))
nv_dunif(x, min = lower, max = upper)
#> AnvlArray
#>  1.0000
#>  0.5000
#>  1.0000
#>  0.5000
#>  1.0000
#> [ CPUf32{5} ] 

nv_punif(x)
#> AnvlArray
#>  0.0000
#>  0.0000
#>  0.2500
#>  1.0000
#>  1.0000
#> [ CPUf32{5} ] 
nv_punif(x, min = -1, max = 2)
#> AnvlArray
#>  0.1667
#>  0.3333
#>  0.4167
#>  0.6667
#>  0.8333
#> [ CPUf32{5} ] 
nv_punif(x, lower_tail = FALSE)
#> AnvlArray
#>  1.0000
#>  1.0000
#>  0.7500
#>  0.0000
#>  0.0000
#> [ CPUf32{5} ] 
nv_punif(x, log_p = TRUE)
#> AnvlArray
#>     -inf
#>     -inf
#>  -1.3863
#>  -0.0000
#>  -0.0000
#> [ CPUf32{5} ] 

p <- nv_array(c(0.025, 0.5, 0.975))
nv_qunif(p)
#> AnvlArray
#>  0.0250
#>  0.5000
#>  0.9750
#> [ CPUf32{3} ] 
nv_qunif(p, min = -1, max = 2)
#> AnvlArray
#>  -0.9250
#>   0.5000
#>   1.9250
#> [ CPUf32{3} ] 
nv_qunif(p, lower_tail = FALSE)
#> AnvlArray
#>  0.9750
#>  0.5000
#>  0.0250
#> [ CPUf32{3} ] 
nv_qunif(nv_array(c(-700, -2, -0.1), dtype = "f64"), log_p = TRUE)
#> AnvlArray
#>  9.8597e-305
#>   1.3534e-01
#>   9.0484e-01
#> [ CPUf64{3} ]