Comprehensive verification suite for the marginal PMF module.
Examples
verify_pmf_marginal_all()
#> ======================================================================
#> Module 06: Marginal PMF - Full Verification Suite
#> ======================================================================
#>
#>
#> [Test case: J=50, a=1.50, b=0.50]
#> --------------------------------------------------
#> Marginal PMF Properties (J=50, a=1.50, b=0.50):
#> Sum = 1: PASS (sum = 1.000000000000)
#> P(K=0) = 0: PASS (P(K=0) = 0.00e+00)
#> Non-negative: PASS (min = 0.00e+00)
#> CDF monotonic: PASS
#> CDF[J] = 1: PASS (CDF[J] = 1.000000000000)
#> Overall: PASS
#> Moments Consistency (J=50, a=1.50, b=0.50):
#> Mean (PMF): 8.35548676
#> Mean (quadrature):8.35548676
#> Mean error: 7.11e-15 [PASS]
#> Var (PMF): 22.76895012
#> Var (quadrature): 22.76895012
#> Var error: 4.26e-14 [PASS]
#> Overall: PASS
#>
#> [Test case: J=50, a=2.00, b=1.00]
#> --------------------------------------------------
#> Marginal PMF Properties (J=50, a=2.00, b=1.00):
#> Sum = 1: PASS (sum = 1.000000000000)
#> P(K=0) = 0: PASS (P(K=0) = 0.00e+00)
#> Non-negative: PASS (min = 0.00e+00)
#> CDF monotonic: PASS
#> CDF[J] = 1: PASS (CDF[J] = 1.000000000000)
#> Overall: PASS
#> Moments Consistency (J=50, a=2.00, b=1.00):
#> Mean (PMF): 6.63969289
#> Mean (quadrature):6.63969289
#> Mean error: 7.99e-15 [PASS]
#> Var (PMF): 12.95450229
#> Var (quadrature): 12.95450229
#> Var error: 8.53e-14 [PASS]
#> Overall: PASS
#>
#> [Test case: J=100, a=1.50, b=0.50]
#> --------------------------------------------------
#> Marginal PMF Properties (J=100, a=1.50, b=0.50):
#> Sum = 1: PASS (sum = 1.000000000000)
#> P(K=0) = 0: PASS (P(K=0) = 0.00e+00)
#> Non-negative: PASS (min = 0.00e+00)
#> CDF monotonic: PASS
#> CDF[J] = 1: PASS (CDF[J] = 1.000000000000)
#> Overall: PASS
#> Moments Consistency (J=100, a=1.50, b=0.50):
#> Mean (PMF): 10.31191600
#> Mean (quadrature):10.31191600
#> Mean error: 2.84e-14 [PASS]
#> Var (PMF): 39.26043331
#> Var (quadrature): 39.26043331
#> Var error: 1.42e-14 [PASS]
#> Overall: PASS
#>
#> [Test case: J=30, a=1.00, b=0.50]
#> --------------------------------------------------
#> Marginal PMF Properties (J=30, a=1.00, b=0.50):
#> Sum = 1: PASS (sum = 1.000000000000)
#> P(K=0) = 0: PASS (P(K=0) = 0.00e+00)
#> Non-negative: PASS (min = 0.00e+00)
#> CDF monotonic: PASS
#> CDF[J] = 1: PASS (CDF[J] = 1.000000000000)
#> Overall: PASS
#> Moments Consistency (J=30, a=1.00, b=0.50):
#> Mean (PMF): 5.37852414
#> Mean (quadrature):5.37852414
#> Mean error: 8.88e-16 [PASS]
#> Var (PMF): 12.35202849
#> Var (quadrature): 12.35202849
#> Var error: 2.84e-14 [PASS]
#> Overall: PASS
#>
#> [Test case: J=50, a=3.00, b=1.50]
#> --------------------------------------------------
#> Marginal PMF Properties (J=50, a=3.00, b=1.50):
#> Sum = 1: PASS (sum = 1.000000000000)
#> P(K=0) = 0: PASS (P(K=0) = 0.00e+00)
#> Non-negative: PASS (min = 0.00e+00)
#> CDF monotonic: PASS
#> CDF[J] = 1: PASS (CDF[J] = 1.000000000000)
#> Overall: PASS
#> Moments Consistency (J=50, a=3.00, b=1.50):
#> Mean (PMF): 6.76261555
#> Mean (quadrature):6.76261555
#> Mean error: 7.99e-15 [PASS]
#> Var (PMF): 10.44232545
#> Var (quadrature): 10.44232545
#> Var error: 1.21e-13 [PASS]
#> Overall: PASS
#>
#> [Convergence test]
#> --------------------------------------------------
#> Quadrature Convergence (J=50, a=1.50, b=0.50):
#> M mean var mean_chg var_chg L1_chg
#> 20 8.35549735 22.76870932 0.00e+00 0.00e+00 0.00e+00
#> 40 8.35548682 22.76894879 1.05e-05 2.39e-04 4.09e-03
#> 80 8.35548676 22.76895012 5.91e-08 1.34e-06 7.89e-05
#> 120 8.35548676 22.76895013 3.75e-11 8.48e-10 8.62e-08
#>
#> ======================================================================
#> Overall Result: ALL TESTS PASSED
#> ======================================================================