tmp/tmpu2jyqmu0/{from.md → to.md}
RENAMED
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@@ -117,11 +117,11 @@ $$%
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The n+1 distribution parameters bᵢ, also known as this distribution’s
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*interval boundaries* , shall satisfy the relation bᵢ < bᵢ₊₁ for
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i = 0, …, n-1. Unless specified otherwise, the remaining n distribution
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parameters are calculated as: $$%
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\rho_k = \;
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-
{w_k
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\; \mbox{ for } k = 0, \ldots, n\!-\!1,$$ in which the values wₖ,
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commonly known as the *weights* , shall be non-negative, non-NaN, and
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non-infinity. Moreover, the following relation shall hold:
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0 < S = w₀ + ⋯ + wₙ₋₁.
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@@ -245,12 +245,12 @@ k = 0, …, n-1.
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A `piecewise_linear_distribution` random number distribution produces
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random numbers x, b₀ ≤ x < bₙ, distributed over each subinterval
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[ bᵢ, bᵢ₊₁ ) according to the probability density function $$%
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p(x\,|\,b_0,\ldots,b_n,\;\rho_0,\ldots,\rho_n)
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= \rho_i \cdot {{b_{i+1} - x}
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+ \rho_{i+1} \cdot {{x - b_i}
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\; \mbox{,}
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\mbox{ for } b_i \le x < b_{i+1}
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\; \mbox{.}$$
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| 256 |
The n+1 distribution parameters bᵢ, also known as this distribution’s
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| 117 |
The n+1 distribution parameters bᵢ, also known as this distribution’s
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| 118 |
*interval boundaries* , shall satisfy the relation bᵢ < bᵢ₊₁ for
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| 119 |
i = 0, …, n-1. Unless specified otherwise, the remaining n distribution
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| 120 |
parameters are calculated as: $$%
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\rho_k = \;
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+
\frac{w_k}{S \cdot (b_{k+1}-b_k)}
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| 123 |
\; \mbox{ for } k = 0, \ldots, n\!-\!1,$$ in which the values wₖ,
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| 124 |
commonly known as the *weights* , shall be non-negative, non-NaN, and
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| 125 |
non-infinity. Moreover, the following relation shall hold:
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| 126 |
0 < S = w₀ + ⋯ + wₙ₋₁.
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| 127 |
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| 245 |
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| 246 |
A `piecewise_linear_distribution` random number distribution produces
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| 247 |
random numbers x, b₀ ≤ x < bₙ, distributed over each subinterval
|
| 248 |
[ bᵢ, bᵢ₊₁ ) according to the probability density function $$%
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| 249 |
p(x\,|\,b_0,\ldots,b_n,\;\rho_0,\ldots,\rho_n)
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+
= \rho_i \cdot {\frac{b_{i+1} - x}{b_{i+1} - b_i}}
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+
+ \rho_{i+1} \cdot {\frac{x - b_i}{b_{i+1} - b_i}}
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\; \mbox{,}
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\mbox{ for } b_i \le x < b_{i+1}
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\; \mbox{.}$$
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| 255 |
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| 256 |
The n+1 distribution parameters bᵢ, also known as this distribution’s
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