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Copy file name to clipboardExpand all lines: lib/node_modules/@stdlib/random/base/box-muller/lib/randn.js
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/**
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* Generates a standard normally distributed random number.
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*
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* #### Method
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* ## Method
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*
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* * Given two independent uniformly distributed random variables \\( U_1 \\) and \\( U_2 \\) in the interval \\( [0,1) \\), let
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* - Given two independent uniformly distributed random variables \\( U_1 \\) and \\( U_2 \\) in the interval \\( [0,1) \\), let
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*
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* ``` tex
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* \begin{align*}
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*
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* where \\( Z_1 \\) and \\( Z_2 \\) are independent random variables with a standard normal distribution.
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*
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* * As two uniform random variates are mapped to two standard normal random variates, one of the random variates is cached and returned upon the following invocation.
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* - As two uniform random variates are mapped to two standard normal random variates, one of the random variates is cached and returned upon the following invocation.
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*
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*
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* #### Notes
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* ## Notes
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*
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* * The minimum and maximum pseudorandom numbers which can be generated are dependent on the number of bits an underlying uniform pseudorandom number generator (PRNG) uses. For instance, if a PRNG uses \\( 32 \\) bits, the smallest non-zero number that can be generated is \\( 2^{-32}). When \\( U_1 \\) equals this value and \\( U_2 \\) equals \\( 0 \\),
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* - The minimum and maximum pseudorandom numbers which can be generated are dependent on the number of bits an underlying uniform pseudorandom number generator (PRNG) uses. For instance, if a PRNG uses \\( 32 \\) bits, the smallest non-zero number that can be generated is \\( 2^{-32}). When \\( U_1 \\) equals this value and \\( U_2 \\) equals \\( 0 \\),
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*
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* ``` tex
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* r = \sqrt{-2\ln(2^{-32})} \cos(2\pi) \approx 6.66
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* <!-- </note> -->
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*
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*
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* #### References
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* ## References
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*
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* * Box, G. E. P., and Mervin E. Muller. 1958. "A Note on the Generation of Random Normal Deviates." *The Annals of Mathematical Statistics* 29 (2). The Institute of Mathematical Statistics: 610–11. doi:[10.1214/aoms/1177706645](http://dx.doi.org/10.1214/aoms/1177706645).
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* * Bell, James R. 1968. "Algorithm 334: Normal Random Deviates." *Communications of the ACM* 11 (7). New York, NY, USA: ACM: 498. doi:[10.1145/363397.363547](http://dx.doi.org/10.1145/363397.363547).
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* * Knop, R. 1969. "Remark on Algorithm 334 [G5]: Normal Random Deviates." *Communications of the ACM* 12 (5). New York, NY, USA: ACM: 281. doi:[10.1145/362946.362996](http://dx.doi.org/10.1145/362946.362996).
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* * Marsaglia, G., and T. A. Bray. 1964. "A Convenient Method for Generating Normal Variables." *SIAM Review* 6 (3). Society for Industrial; Applied Mathematics: 260–64. doi:[10.1137/1006063](http://dx.doi.org/10.1137/1006063).
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* * Thomas, David B., Wayne Luk, Philip H.W. Leong, and John D. Villasenor. 2007. "Gaussian Random Number Generators." *ACM Computing Surveys* 39 (4). New York, NY, USA: ACM. doi:[10.1145/1287620.1287622](http://dx.doi.org/10.1145/1287620.1287622).
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* - Box, G. E. P., and Mervin E. Muller. 1958. "A Note on the Generation of Random Normal Deviates." _The Annals of Mathematical Statistics_ 29 (2). The Institute of Mathematical Statistics: 610–11. doi:[10.1214/aoms/1177706645](http://dx.doi.org/10.1214/aoms/1177706645).
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* - Bell, James R. 1968. "Algorithm 334: Normal Random Deviates." *Communications of the ACM* 11 (7). New York, NY, USA: ACM: 498. doi:[10.1145/363397.363547](http://dx.doi.org/10.1145/363397.363547).
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* - Knop, R. 1969. "Remark on Algorithm 334 [G5]: Normal Random Deviates." _Communications of the ACM_ 12 (5). New York, NY, USA: ACM: 281. doi:[10.1145/362946.362996](http://dx.doi.org/10.1145/362946.362996).
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* - Marsaglia, G., and T. A. Bray. 1964. "A Convenient Method for Generating Normal Variables." _SIAM Review_ 6 (3). Society for Industrial; Applied Mathematics: 260–64. doi:[10.1137/1006063](http://dx.doi.org/10.1137/1006063).
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* - Thomas, David B., Wayne Luk, Philip H.W. Leong, and John D. Villasenor. 2007. "Gaussian Random Number Generators." _ACM Computing Surveys_ 39 (4). New York, NY, USA: ACM. doi:[10.1145/1287620.1287622](http://dx.doi.org/10.1145/1287620.1287622).
Copy file name to clipboardExpand all lines: lib/node_modules/@stdlib/random/sample/lib/vose.js
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@@ -30,7 +30,7 @@ var floor = require( '@stdlib/math/base/special/floor' );
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*
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* ## References
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*
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* - Vose, Michael D. 1991. "A linear algorithm for generating random numbers with a given distribution." *IEEE Transactions on Software Engineering* 17 (9): 972–75. doi:[10.1109/32.92917][@vose:1991].
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* - Vose, Michael D. 1991. "A linear algorithm for generating random numbers with a given distribution." _IEEE Transactions on Software Engineering_ 17 (9): 972–75. doi:[10.1109/32.92917][@vose:1991].
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