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add yule_simon_rng#3285

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lingium:feature/issue-3239-yule-simon-rng
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add yule_simon_rng#3285
lingium wants to merge 4 commits intostan-dev:developfrom
lingium:feature/issue-3239-yule-simon-rng

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@lingium lingium commented Feb 22, 2026

Summary

With this PR the rng of Yule-Simon distribution are added.
See issue #3239

For $$Y\sim \text{Yule-Simon}(\alpha)$$:

$$ \Pr(Y=y\mid \alpha)= \alpha \mathrm{B}(y,\alpha+1) \quad y\in{1,2,\dots} $$

$$\mathrm{B}$$ is the Beta function.

It has a Beta–Geometric mixture. To sample form $$Y$$, we do:

$$ \begin{align} Y\mid p &\sim \text{Geometric}(p)\\ p=e^{-W} &\sim \text{Beta}(\alpha,1)\\ W &\sim\text{Exp}(\alpha) \end{align} $$

Stan does not have Geometric yet so we use neg_binomial_rng(1.0, odds_ratio_p).

Tests

Test is written follow the guide.

Side Effects

No.

Release notes

yule_simon_rng is available if merged.

Checklist

  • Copyright holder: Zhi Ling

    The copyright holder is typically you or your assignee, such as a university or company. By submitting this pull request, the copyright holder is agreeing to the license the submitted work under the following licenses:
    - Code: BSD 3-clause (https://opensource.org/licenses/BSD-3-Clause)
    - Documentation: CC-BY 4.0 (https://creativecommons.org/licenses/by/4.0/)

  • the basic tests are passing

    • unit tests pass (to run, use: ./runTests.py test/unit)
    • header checks pass, (make test-headers)
    • dependencies checks pass, (make test-math-dependencies)
    • docs build, (make doxygen)
    • code passes the built in C++ standards checks (make cpplint)

  • the code is written in idiomatic C++ and changes are documented in the doxygen

  • the new changes are tested

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stan-buildbot commented Feb 22, 2026

Name Old Result New Result Ratio Performance change( 1 - new / old )
gp_regr/gp_regr.stan 0.09 0.09 1.0 0.43% faster
gp_regr/gen_gp_data.stan 0.02 0.02 0.98 -2.31% slower
arK/arK.stan 1.71 1.71 1.0 -0.01% slower
eight_schools/eight_schools.stan 0.05 0.05 1.02 2.13% faster
low_dim_gauss_mix_collapse/low_dim_gauss_mix_collapse.stan 8.38 8.39 1.0 -0.13% slower
pkpd/one_comp_mm_elim_abs.stan 18.66 18.72 1.0 -0.32% slower
pkpd/sim_one_comp_mm_elim_abs.stan 0.24 0.24 1.01 0.69% faster
sir/sir.stan 66.0 65.84 1.0 0.24% faster
gp_pois_regr/gp_pois_regr.stan 2.68 2.68 1.0 -0.15% slower
low_dim_gauss_mix/low_dim_gauss_mix.stan 2.68 2.56 1.05 4.54% faster
irt_2pl/irt_2pl.stan 3.93 3.93 1.0 -0.03% slower
arma/arma.stan 0.28 0.27 1.01 0.52% faster
garch/garch.stan 0.4 0.4 1.0 -0.47% slower
low_dim_corr_gauss/low_dim_corr_gauss.stan 0.01 0.01 1.0 0.1% faster
performance.compilation 224.23 223.79 1.0 0.2% faster
Mean result: 1.0038365452200027

Jenkins Console Log
Blue Ocean
Commit hash: 19930437e3538fa8e0be8b788055ba897f63efce

Machine information No LSB modules are available. Distributor ID: Ubuntu Description: Ubuntu 20.04.3 LTS Release: 20.04 Codename: focal

CPU:
Architecture: x86_64
CPU op-mode(s): 32-bit, 64-bit
Byte Order: Little Endian
Address sizes: 46 bits physical, 48 bits virtual
CPU(s): 80
On-line CPU(s) list: 0-79
Thread(s) per core: 2
Core(s) per socket: 20
Socket(s): 2
NUMA node(s): 2
Vendor ID: GenuineIntel
CPU family: 6
Model: 85
Model name: Intel(R) Xeon(R) Gold 6148 CPU @ 2.40GHz
Stepping: 4
CPU MHz: 2400.000
CPU max MHz: 3700.0000
CPU min MHz: 1000.0000
BogoMIPS: 4800.00
Virtualization: VT-x
L1d cache: 1.3 MiB
L1i cache: 1.3 MiB
L2 cache: 40 MiB
L3 cache: 55 MiB
NUMA node0 CPU(s): 0,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78
NUMA node1 CPU(s): 1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,53,55,57,59,61,63,65,67,69,71,73,75,77,79
Vulnerability Gather data sampling: Mitigation; Microcode
Vulnerability Itlb multihit: KVM: Mitigation: VMX disabled
Vulnerability L1tf: Mitigation; PTE Inversion; VMX conditional cache flushes, SMT vulnerable
Vulnerability Mds: Mitigation; Clear CPU buffers; SMT vulnerable
Vulnerability Meltdown: Mitigation; PTI
Vulnerability Mmio stale data: Mitigation; Clear CPU buffers; SMT vulnerable
Vulnerability Reg file data sampling: Not affected
Vulnerability Retbleed: Mitigation; IBRS
Vulnerability Spec rstack overflow: Not affected
Vulnerability Spec store bypass: Mitigation; Speculative Store Bypass disabled via prctl
Vulnerability Spectre v1: Mitigation; usercopy/swapgs barriers and __user pointer sanitization
Vulnerability Spectre v2: Mitigation; IBRS; IBPB conditional; STIBP conditional; RSB filling; PBRSB-eIBRS Not affected; BHI Not affected
Vulnerability Srbds: Not affected
Vulnerability Tsx async abort: Mitigation; Clear CPU buffers; SMT vulnerable
Vulnerability Vmscape: Mitigation; IBPB before exit to userspace
Flags: fpu vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov pat pse36 clflush dts acpi mmx fxsr sse sse2 ss ht tm pbe syscall nx pdpe1gb rdtscp lm constant_tsc art arch_perfmon pebs bts rep_good nopl xtopology nonstop_tsc cpuid aperfmperf pni pclmulqdq dtes64 monitor ds_cpl vmx smx est tm2 ssse3 sdbg fma cx16 xtpr pdcm pcid dca sse4_1 sse4_2 x2apic movbe popcnt tsc_deadline_timer aes xsave avx f16c rdrand lahf_lm abm 3dnowprefetch cpuid_fault epb cat_l3 cdp_l3 invpcid_single pti intel_ppin ssbd mba ibrs ibpb stibp tpr_shadow vnmi flexpriority ept vpid ept_ad fsgsbase tsc_adjust bmi1 hle avx2 smep bmi2 erms invpcid rtm cqm mpx rdt_a avx512f avx512dq rdseed adx smap clflushopt clwb intel_pt avx512cd avx512bw avx512vl xsaveopt xsavec xgetbv1 xsaves cqm_llc cqm_occup_llc cqm_mbm_total cqm_mbm_local dtherm ida arat pln pts hwp hwp_act_window hwp_epp hwp_pkg_req pku ospke md_clear flush_l1d arch_capabilities

G++:
g++ (Ubuntu 9.4.0-1ubuntu1~20.04) 9.4.0
Copyright (C) 2019 Free Software Foundation, Inc.
This is free software; see the source for copying conditions. There is NO
warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

Clang:
clang version 10.0.0-4ubuntu1
Target: x86_64-pc-linux-gnu
Thread model: posix
InstalledDir: /usr/bin

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lingium commented Feb 23, 2026

Rtools & ARM64 CI / rev tests (windows-11-arm) (pull_request)

[----------] 11 tests from StanOde/cos_arg_test/4, where TypeParam = std::tuple<ode_adjoint_functor, ode_adjoint_functor>
[ RUN      ] StanOde/cos_arg_test/4.y0_error
[       OK ] StanOde/cos_arg_test/4.y0_error (0 ms)
[ RUN      ] StanOde/cos_arg_test/4.t0_error
[       OK ] StanOde/cos_arg_test/4.t0_error (0 ms)
[ RUN      ] StanOde/cos_arg_test/4.ts_error
[       OK ] StanOde/cos_arg_test/4.ts_error (1 ms)
[ RUN      ] StanOde/cos_arg_test/4.one_arg_error
[       OK ] StanOde/cos_arg_test/4.one_arg_error (1 ms)
[ RUN      ] StanOde/cos_arg_test/4.two_arg_error
[       OK ] StanOde/cos_arg_test/4.two_arg_error (2 ms)
[ RUN      ] StanOde/cos_arg_test/4.rhs_wrong_size_error
[       OK ] StanOde/cos_arg_test/4.rhs_wrong_size_error (0 ms)
[ RUN      ] StanOde/cos_arg_test/4.error_name
[       OK ] StanOde/cos_arg_test/4.error_name (0 ms)
[ RUN      ] StanOde/cos_arg_test/4.tol_error
[       OK ] StanOde/cos_arg_test/4.tol_error (0 ms)
[ RUN      ] StanOde/cos_arg_test/4.value
[       OK ] StanOde/cos_arg_test/4.value (0 ms)
[ RUN      ] StanOde/cos_arg_test/4.grad
[       OK ] StanOde/cos_arg_test/4.grad (6 ms)
[ RUN      ] StanOde/cos_arg_test/4.tol_grad
./test/unit/math/rev/functor/test_fixture_ode_cos_scalar.hpp:1317: Failure
Expected equality of these values:
  a.adj()
    Which is: -0.43164793
  -0.5 * (tsd[0] * tsd[0] - t0d * t0d) * y0d(0) * exp(-0.5 * ad * (tsd[0] * tsd[0] - t0d * t0d))
    Which is: -0.43164769
[  FAILED  ] StanOde/cos_arg_test/4.tol_grad, where TypeParam = std::tuple<ode_adjoint_functor, ode_adjoint_functor> (5 ms)
[----------] 11 tests from StanOde/cos_arg_test/4 (15 ms total)

[----------] Global test environment tear-down
[==========] 55 tests from 5 test suites ran. (37 ms total)
[  PASSED  ] 54 tests.
[  FAILED  ] 1 test, listed below:
[  FAILED  ] StanOde/cos_arg_test/4.tol_grad, where TypeParam = std::tuple<ode_adjoint_functor, ode_adjoint_functor>

 1 FAILED TEST
test\unit\math\rev\functor\cos_ode_typed_test.exe --gtest_output="xml:test/unit/math/rev/functor/cos_ode_typed_test.xml" failed

Seems a test on ode fails, but this might be unrelated to this PR? My mac can pass the rev tests.

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WardBrian commented Feb 23, 2026

@lingium it passed on re-run, so I think it was just random noise

SteveBronder
SteveBronder previously approved these changes Feb 23, 2026
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Two minor comments but imo looks good!

stan/math/prim/prob/yule_simon_rng.hpp Outdated
Comment on lines 39 to 50
scalar_seq_view<T_w> w_vec(w);
size_t size_w = stan::math::size(w);

VectorBuilder<true, int, T_alpha> output(size_w);
for (size_t n = 0; n < size_w; ++n) {
double p = stan::math::exp(-w_vec.val(n));
double odds_ratio_p
= stan::math::exp(stan::math::log(p) - stan::math::log1m(p));
output[n] = neg_binomial_rng(1.0, odds_ratio_p, rng) + 1;
}

return output.data();
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Since you use neg_binomial_rng I think we can use the vectorized version of everything here

Suggested change
scalar_seq_view<T_w> w_vec(w);
size_t size_w = stan::math::size(w);
VectorBuilder<true, int, T_alpha> output(size_w);
for (size_t n = 0; n < size_w; ++n) {
double p = stan::math::exp(-w_vec.val(n));
double odds_ratio_p
= stan::math::exp(stan::math::log(p) - stan::math::log1m(p));
output[n] = neg_binomial_rng(1.0, odds_ratio_p, rng) + 1;
}
return output.data();
auto p = stan::math::exp(-w);
auto odds_ratio_p = stan::math::exp(stan::math::log(p) - stan::math::log1m(p));
return neg_binomial_rng(1.0, odds_ratio_p, rng) + 1;

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@lingium lingium Feb 24, 2026

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Seems neg_binomial_rng(...) + 1; cannot pass compile, let's keep the loop version?

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stan-buildbot commented Feb 24, 2026

Name Old Result New Result Ratio Performance change( 1 - new / old )
gp_regr/gp_regr.stan 0.13 0.1 1.34 25.64% faster
gp_regr/gen_gp_data.stan 0.03 0.03 1.0 0.04% faster
arK/arK.stan 1.88 1.85 1.02 1.59% faster
eight_schools/eight_schools.stan 0.06 0.06 1.0 -0.16% slower
low_dim_gauss_mix_collapse/low_dim_gauss_mix_collapse.stan 9.17 9.06 1.01 1.2% faster
pkpd/one_comp_mm_elim_abs.stan 20.32 20.25 1.0 0.31% faster
pkpd/sim_one_comp_mm_elim_abs.stan 0.26 0.28 0.93 -7.05% slower
sir/sir.stan 71.69 71.86 1.0 -0.24% slower
gp_pois_regr/gp_pois_regr.stan 2.9 2.91 0.99 -0.55% slower
low_dim_gauss_mix/low_dim_gauss_mix.stan 2.76 2.78 1.0 -0.48% slower
irt_2pl/irt_2pl.stan 4.42 4.41 1.0 0.38% faster
arma/arma.stan 0.31 0.3 1.01 1.14% faster
garch/garch.stan 0.45 0.45 1.0 -0.21% slower
low_dim_corr_gauss/low_dim_corr_gauss.stan 0.01 0.01 0.95 -5.63% slower
performance.compilation 251.33 248.87 1.01 0.98% faster
Mean result: 1.0177538324870377

Jenkins Console Log
Blue Ocean
Commit hash: 19930437e3538fa8e0be8b788055ba897f63efce

Machine information No LSB modules are available. Distributor ID: Ubuntu Description: Ubuntu 20.04.3 LTS Release: 20.04 Codename: focal

CPU:
Architecture: x86_64
CPU op-mode(s): 32-bit, 64-bit
Byte Order: Little Endian
Address sizes: 46 bits physical, 48 bits virtual
CPU(s): 80
On-line CPU(s) list: 0-79
Thread(s) per core: 2
Core(s) per socket: 20
Socket(s): 2
NUMA node(s): 2
Vendor ID: GenuineIntel
CPU family: 6
Model: 85
Model name: Intel(R) Xeon(R) Gold 6148 CPU @ 2.40GHz
Stepping: 4
CPU MHz: 2400.000
CPU max MHz: 3700.0000
CPU min MHz: 1000.0000
BogoMIPS: 4800.00
Virtualization: VT-x
L1d cache: 1.3 MiB
L1i cache: 1.3 MiB
L2 cache: 40 MiB
L3 cache: 55 MiB
NUMA node0 CPU(s): 0,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78
NUMA node1 CPU(s): 1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,53,55,57,59,61,63,65,67,69,71,73,75,77,79
Vulnerability Gather data sampling: Mitigation; Microcode
Vulnerability Itlb multihit: KVM: Mitigation: VMX disabled
Vulnerability L1tf: Mitigation; PTE Inversion; VMX conditional cache flushes, SMT vulnerable
Vulnerability Mds: Mitigation; Clear CPU buffers; SMT vulnerable
Vulnerability Meltdown: Mitigation; PTI
Vulnerability Mmio stale data: Mitigation; Clear CPU buffers; SMT vulnerable
Vulnerability Reg file data sampling: Not affected
Vulnerability Retbleed: Mitigation; IBRS
Vulnerability Spec rstack overflow: Not affected
Vulnerability Spec store bypass: Mitigation; Speculative Store Bypass disabled via prctl
Vulnerability Spectre v1: Mitigation; usercopy/swapgs barriers and __user pointer sanitization
Vulnerability Spectre v2: Mitigation; IBRS; IBPB conditional; STIBP conditional; RSB filling; PBRSB-eIBRS Not affected; BHI Not affected
Vulnerability Srbds: Not affected
Vulnerability Tsx async abort: Mitigation; Clear CPU buffers; SMT vulnerable
Vulnerability Vmscape: Mitigation; IBPB before exit to userspace
Flags: fpu vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov pat pse36 clflush dts acpi mmx fxsr sse sse2 ss ht tm pbe syscall nx pdpe1gb rdtscp lm constant_tsc art arch_perfmon pebs bts rep_good nopl xtopology nonstop_tsc cpuid aperfmperf pni pclmulqdq dtes64 monitor ds_cpl vmx smx est tm2 ssse3 sdbg fma cx16 xtpr pdcm pcid dca sse4_1 sse4_2 x2apic movbe popcnt tsc_deadline_timer aes xsave avx f16c rdrand lahf_lm abm 3dnowprefetch cpuid_fault epb cat_l3 cdp_l3 invpcid_single pti intel_ppin ssbd mba ibrs ibpb stibp tpr_shadow vnmi flexpriority ept vpid ept_ad fsgsbase tsc_adjust bmi1 hle avx2 smep bmi2 erms invpcid rtm cqm mpx rdt_a avx512f avx512dq rdseed adx smap clflushopt clwb intel_pt avx512cd avx512bw avx512vl xsaveopt xsavec xgetbv1 xsaves cqm_llc cqm_occup_llc cqm_mbm_total cqm_mbm_local dtherm ida arat pln pts hwp hwp_act_window hwp_epp hwp_pkg_req pku ospke md_clear flush_l1d arch_capabilities

G++:
g++ (Ubuntu 9.4.0-1ubuntu1~20.04) 9.4.0
Copyright (C) 2019 Free Software Foundation, Inc.
This is free software; see the source for copying conditions. There is NO
warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

Clang:
clang version 10.0.0-4ubuntu1
Target: x86_64-pc-linux-gnu
Thread model: posix
InstalledDir: /usr/bin

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