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Commit e7984cb

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reintroduced old interface through wrappers and updated specs
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‎doc/specs/stdlib_stats_distribution_exponential.md‎

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@@ -15,14 +15,19 @@ Experimental
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### Description
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An exponential distribution is the distribution of time between events in a Poisson point process.
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The inverse scale parameter `lambda` specifies the average time between events (\(\lambda\)), also called the rate of events.
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The inverse `scale` parameter `lambda` specifies the average time between events (\(\lambda\)), also called the rate of events. The location `loc` specifies the value by which the distribution is shifted.
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Without argument, the function returns a random sample from the standard exponential distribution \(E(\lambda=1)\).
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Without argument, the function returns a random sample from the unshifted standard exponential distribution \(E(\lambda=1)\) or \(E(loc=0, scale=1)\).
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With a single argument, the function returns a random sample from the exponential distribution \(E(\lambda=\text{lambda})\).
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With a single argument of type `real`, the function returns a random sample from the exponential distribution \(E(\lambda=\text{lambda})\).
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For complex arguments, the real and imaginary parts are sampled independently of each other.
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With two arguments, the function returns a rank-1 array of exponentially distributed random variates.
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With one argument of type `real` and one argument of type `integer`, the function returns a rank-1 array of exponentially distributed random variates for (E(\lambda=\text{lambda})\).
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With two arguments of type `real`, the function returns a random sample from the exponential distribution \(E(loc=loc, scale=scale)\).
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For complex arguments, the real and imaginary parts are sampled independently of each other.
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With two arguments of type `real` and one argument of type `integer`, the function returns a rank-1 array of exponentially distributed random variates for \(E(loc=loc, scale=scale)\).
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@note
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The algorithm used for generating exponential random variates is fundamentally limited to double precision.[^1]
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`result = ` [[stdlib_stats_distribution_exponential(module):rvs_exp(interface)]] `([lambda] [[, array_size]])`
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or
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`result = ` [[stdlib_stats_distribution_exponential(module):rvs_exp(interface)]] `([loc, scale] [[, array_size]])`
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### Class
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Elemental function
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`lambda`: optional argument has `intent(in)` and is a scalar of type `real` or `complex`.
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If `lambda` is `real`, its value must be positive. If `lambda` is `complex`, both the real and imaginary components must be positive.
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`loc`: optional argument has `intent(in)` and is a scalar of type `real` or `complex`.
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`scale`: optional argument has `intent(in)` and is a positive scalar of type `real` or `complex`.
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If `scale` is `real`, its value must be positive. If `scale` is `complex`, both the real and imaginary components must be positive.
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`array_size`: optional argument has `intent(in)` and is a scalar of type `integer` with default kind.
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### Return value
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The result is a scalar or rank-1 array with a size of `array_size`, and the same type as `lambda`.
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If `lambda` is passed, the result is a scalar or rank-1 array with a size of `array_size`, and the same type as `lambda`.
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If `lambda` is non-positive, the result is `NaN`.
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If `loc` and `scale` are passed, the result is a scalar or rank-1 array with a size of `array_size`, and the same type as `scale`.
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If `scale` is non-positive, the result is `NaN`.
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### Example
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```fortran
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$$f(x+\mathit{i}y)=f(x)f(y)=\begin{cases} \lambda_{x} \lambda_{y} e^{-(\lambda_{x} x + \lambda_{y} y)} &x\geqslant 0, y\geqslant 0 \\\\ 0 &\text{otherwise}\end{cases}$$
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Instead of of the inverse scale parameter `lambda`, it is possible to pass `loc` and `scale`, where \(scale = \frac{1}{\lambda}\) and `loc` specifies the value by which the distribution is shifted.
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### Syntax
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`result = ` [[stdlib_stats_distribution_exponential(module):pdf_exp(interface)]] `(x, lambda)`
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or
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`result = ` [[stdlib_stats_distribution_exponential(module):pdf_exp(interface)]] `(x, loc, scale)`
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### Class
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Elemental function
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`lambda`: has `intent(in)` and is a scalar of type `real` or `complex`.
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If `lambda` is `real`, its value must be positive. If `lambda` is `complex`, both the real and imaginary components must be positive.
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`loc`: has `intent(in)` and is a scalar of type `real` or `complex`.
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`scale`: has `intent(in)` and is a positive scalar of type `real` or `complex`.
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If `scale` is `real`, its value must be positive. If `scale` is `complex`, both the real and imaginary components must be positive.
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All arguments must have the same type.
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### Return value
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The result is a scalar or an array, with a shape conformable to the arguments, and the same type as the input arguments. If `lambda` is non-positive, the result is `NaN`.
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If `lambda` is passed, the result is a scalar or an array, with a shape conformable to the arguments, and the same type as the input arguments. If `lambda` is non-positive, the result is `NaN`.
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If `loc` and `scale` are passed, the result is a scalar or an array, with a shape conformable to the arguments, and the same type as the input arguments. If `scale` is non-positive, the result is `NaN`.
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### Example
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$$F(x+\mathit{i}y)=F(x)F(y)=\begin{cases} (1 - e^{-\lambda_{x} x})(1 - e^{-\lambda_{y} y}) &x\geqslant 0, \;\; y\geqslant 0 \\\\ 0 & \text{otherwise} \end{cases}$$
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Instead of of the inverse scale parameter `lambda`, it is possible to pass `loc` and `scale`, where \(scale = \frac{1}{\lambda}\) and `loc` specifies the value by which the distribution is shifted.
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### Syntax
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`result = ` [[stdlib_stats_distribution_exponential(module):cdf_exp(interface)]] `(x, lambda)`
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or
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`result = ` [[stdlib_stats_distribution_exponential(module):cdf_exp(interface)]] `(x, loc, scale)`
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### Class
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Elemental function
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`lambda`: has `intent(in)` and is a scalar of type `real` or `complex`.
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If `lambda` is `real`, its value must be positive. If `lambda` is `complex`, both the real and imaginary components must be positive.
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`loc`: has `intent(in)` and is a scalar of type `real` or `complex`.
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`scale`: has `intent(in)` and is a positive scalar of type `real` or `complex`.
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If `scale` is `real`, its value must be positive. If `scale` is `complex`, both the real and imaginary components must be positive.
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All arguments must have the same type.
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### Return value
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The result is a scalar or an array, with a shape conformable to the arguments, and the same type as the input arguments. If `lambda` is non-positive, the result is `NaN`.
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If `lamba` is passed, the result is a scalar or an array, with a shape conformable to the arguments, and the same type as the input arguments. If `lambda` is non-positive, the result is `NaN`.
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If `loc` and `scale` are passed, the result is a scalar or an array, with a shape conformable to the arguments, and the same type as the input arguments. If `scale` is non-positive, the result is `NaN`.
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### Example
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‎example/stats_distribution_exponential/example_exponential_cdf.f90‎

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@@ -12,10 +12,18 @@ program example_exponential_cdf
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seed_put = 1234567
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call random_seed(seed_put, seed_get)
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! standard exponential cumulative distribution at x=1.0 with lambda=1.0
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print *, exp_cdf(1.0, 1.0)
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! 0.632120550
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! standard exponential cumulative distribution at x=1.0 with loc=0.0, scale=1.0
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print *, exp_cdf(1.0, 0.0, 1.0)
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! 0.632120550
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! cumulative distribution at x=2.0 with lambda=2
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print *, exp_cdf(2.0, 2.0)
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! 0.981684387
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! cumulative distribution at x=2.0 with loc=0.0 and scale=0.5 (equivalent of lambda=2)
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print *, exp_cdf(2.0, 0.0, 0.5)
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! 0.981684387

‎example/stats_distribution_exponential/example_exponential_pdf.f90‎

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@@ -12,10 +12,18 @@ program example_exponential_pdf
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seed_put = 1234567
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call random_seed(seed_put, seed_get)
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! probability density at x=1.0 with loc=0 and in standard exponential
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! probability density at x=1.0 with lambda=1.0
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print *, exp_pdf(1.0, 1.0)
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! 0.367879450
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! probability density at x=1.0 with loc=0 and scale=1.0
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print *, exp_pdf(1.0, 0.0, 1.0)
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! 0.367879450
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! probability density at x=2.0 with lambda=2.0
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print *, exp_pdf(2.0, 2.0)
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! 3.66312787E-02
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! probability density at x=2.0 with loc=0.0 and scale=0.5 (lambda=2.0)
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print *, exp_pdf(2.0, 0.0, 0.5)
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! 3.66312787E-02

‎example/stats_distribution_exponential/example_exponential_rvs.f90‎

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seed_put = 1234567
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call random_seed(seed_put, seed_get)
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print *, rexp() !single standard exponential random variate
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! 0.358690143
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! single standard exponential random variate
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print *, rexp()
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! 0.358690143
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print *, rexp(0.6, 0.2) !exponential random variate with loc=0.6 and scale=0.5 (lambda=2)
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! 0.681645989
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! exponential random variate with lambda=2
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print *, rexp(2.0)
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! 0.204114929
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print*, rexp(0.0, 3.0, 10) !an array of 10 variates with loc=0.0 and scale=3.0 (lambda=1/3)
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! 0.184008643 0.359742016 1.36567295 2.62772131 0.362352759
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! 5.47133636 2.13591909 0.410784155 5.83882189 6.71128035
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! exponential random variate with loc=0 and scale=0.5 (lambda=2)
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print*, rexp(0.0, 0.5)
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! 0.122672431
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! exponential random variate with loc=0.6 and scale=0.2 (lambda=5)
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print *, rexp(0.6, 0.2)
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! 0.681645989
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! an array of 10 variates with loc=0.0 and scale=3.0 (lambda=1/3)
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print *, rexp(0.0, 3.0, 10)
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! 1.36567295 2.62772131 0.362352759 5.47133636 2.13591909
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! 0.410784155 5.83882189 6.71128035 1.31730068 1.90963650
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! single complex exponential random variate with real part of scale=0.5 (lambda=2.0);
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! imagainary part of scale=1.6 (lambda=0.625)
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cloc = (0.0, 0.0)
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cscale = (0.5, 1.6)
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print *, rexp(cloc, cscale)
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!single complex exponential random variate with real part of scale=0.5 (lambda=2.0);
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!imagainary part of scale=1.6 (lambda=0.625)
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! (0.219550118,1.01847279)
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! (0.426896989,2.56968451)
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end program example_exponential_rvs

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