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* Kolmogorov-Smirnov distribution #421 Add a new distribution, kolmogorov_smirnov_distribution, which takes a parameter that represents the number of observations used in a Kolmogorov-Smirnov test. (The K-S test is a popular test for comparing two CDFs, but the test statistic is not implemented here.) This implementation includes Kolmogorov's original 1st order Taylor expansion. There is a literature on the distribution's other mathematical properties (higher order terms and exact version); this literature is summarized in the main header file for anyone who may want to expand the implementation later. The CDF is implemented using a Jacobi theta function, and the PDF is a hand-rolled derivative of that function. Quantiles plug the CDF and PDF into a Newton-Raphson iteration. The mean and variance have nice closed-form expressions, and the mode uses a dumb run-time maximizer. This commit includes graphs, a ULP plotter for the PDF, and the usual compilation and numerical tests. The test file is on the small side, but it integrates the distribution from zero to infinity, and covers the quantiles pretty well. As of now the numerical tests only verify self-consistency (e.g. distribution moments and CDF-quantile relations), so there's room to add some external checks. * Implement skewness for K-S distribution [CI SKIP] The third moment integrates nicely with the help of Apery's constant (zeta_three). Verify the result via quadrature. * Implement kurtosis for the K-S distribution Verify the result via quadrature.
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16 KiB
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468 lines
16 KiB
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quaternions.html
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math_toolkit/quat_overview.html
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math_toolkit/quat_header.html
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math_toolkit/quat_synopsis.html
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math_toolkit/quat.html
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math_toolkit/spec.html
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math_toolkit/mem_typedef.html
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math_toolkit/quat_mem_fun.html
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math_toolkit/quat_non_mem.html
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math_toolkit/value_op.html
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math_toolkit/create.html
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math_toolkit/trans.html
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math_toolkit/quat_tests.html
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math_toolkit/exp.html
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math_toolkit/acknowledgement.html
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math_toolkit/quat_history.html
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math_toolkit/quat_todo.html
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octonions.html
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math_toolkit/oct_overview.html
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math_toolkit/oct_header.html
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math_toolkit/oct_synopsis.html
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math_toolkit/octonion.html
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math_toolkit/oct_specialization.html
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math_toolkit/oct_typedefs.html
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math_toolkit/oct_mem_fun.html
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math_toolkit/oct_non_mem.html
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math_toolkit/oct_value_ops.html
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math_toolkit/oct_create.html
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math_toolkit/oct_trans.html
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math_toolkit/oct_tests.html
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math_toolkit/acknowledgements.html
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math_toolkit/oct_history.html
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math_toolkit/oct_todo.html
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gcd_lcm.html
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internals.html
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math_toolkit/internals_overview.html
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math_toolkit/internals.html
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math_toolkit/internals/series_evaluation.html
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math_toolkit/internals/cf.html
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math_toolkit/internals/recurrence.html
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math_toolkit/internals/tuples.html
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math_toolkit/internals/minimax.html
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math_toolkit/internals/error_test.html
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math_toolkit/internals/test_data.html
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using_udt.html
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math_toolkit/high_precision.html
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math_toolkit/high_precision/why_high_precision.html
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math_toolkit/high_precision/use_multiprecision.html
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math_toolkit/high_precision/float128.html
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math_toolkit/high_precision/use_mpfr.html
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math_toolkit/high_precision/e_float.html
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math_toolkit/high_precision/use_ntl.html
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math_toolkit/high_precision/using_test.html
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math_toolkit/real_concepts.html
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math_toolkit/dist_concept.html
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math_toolkit/archetypes.html
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policy.html
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math_toolkit/pol_overview.html
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math_toolkit/pol_tutorial.html
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math_toolkit/pol_tutorial/what_is_a_policy.html
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math_toolkit/pol_tutorial/policy_tut_defaults.html
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math_toolkit/pol_tutorial/policy_usage.html
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math_toolkit/pol_tutorial/changing_policy_defaults.html
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math_toolkit/pol_tutorial/ad_hoc_dist_policies.html
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math_toolkit/pol_tutorial/ad_hoc_sf_policies.html
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math_toolkit/pol_tutorial/namespace_policies.html
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math_toolkit/pol_tutorial/user_def_err_pol.html
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math_toolkit/pol_tutorial/understand_dis_quant.html
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math_toolkit/pol_ref.html
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math_toolkit/pol_ref/error_handling_policies.html
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math_toolkit/pol_ref/internal_promotion.html
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math_toolkit/pol_ref/assert_undefined.html
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math_toolkit/pol_ref/discrete_quant_ref.html
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math_toolkit/pol_ref/precision_pol.html
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math_toolkit/pol_ref/iteration_pol.html
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math_toolkit/pol_ref/policy_defaults.html
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math_toolkit/pol_ref/namespace_pol.html
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math_toolkit/pol_ref/pol_ref_ref.html
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perf.html
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math_toolkit/perf_over2.html
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math_toolkit/interp.html
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math_toolkit/getting_best.html
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math_toolkit/tradoffs.html
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math_toolkit/multiprecision.html
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math_toolkit/tuning.html
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math_toolkit/comp_compilers.html
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math_toolkit/comparisons.html
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math_toolkit/perf_test_app.html
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backgrounders.html
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math_toolkit/sf_implementation.html
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math_toolkit/special_tut.html
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math_toolkit/special_tut/special_tut_impl.html
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math_toolkit/special_tut/special_tut_test.html
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math_toolkit/relative_error.html
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math_toolkit/lanczos.html
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math_toolkit/remez.html
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math_toolkit/refs.html
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math_toolkit/logs_and_tables.html
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math_toolkit/logs_and_tables/all_table.html
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math_toolkit/logs_and_tables/logs.html
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status.html
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math_toolkit/history2.html
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math_toolkit/issues.html
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math_toolkit/credits.html
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indexes.html
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indexes/s01.html
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indexes/s02.html
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indexes/s03.html
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indexes/s04.html
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indexes/s05.html
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