PoissonKernelTest#
- class QuadratiK.poisson_kernel_test.PoissonKernelTest(rho, num_iter=300, quantile=0.95, random_state=None, n_jobs=8)#
Class for Poisson kernel-based quadratic distance test of Uniformity on the Sphere
Parameters#
- rhofloat
The value of concentration parameter used for the Poisson kernel function.
- num_iterint, optional
Number of iterations for critical value estimation of U-statistic.
- quantilefloat, optional
The quantile to use for critical value estimation
- random_stateint, None, optional.
Seed for random number generation. Defaults to None
- n_jobsint, optional.
n_jobs specifies the maximum number of concurrently running workers. If 1 is given, no joblib parallelism is used at all, which is useful for debugging. For more information on joblib n_jobs refer to - https://joblib.readthedocs.io/en/latest/generated/joblib.Parallel.html. Defaults to 8.
Attributes#
- test_type_str
The type of test performed on the data
- execution_timefloat
Time taken for the test method to execute
- u_statistic_h0_boolean
A logical value indicating whether or not the null hypothesis is rejected according to Un
- u_statistic_un_float
The value of the U-statistic.
- u_statistic_cv_float
The empirical critical value for Un
- v_statistic_h0_boolean
A logical value indicating whether or not the null hypothesis is rejected according to Vn.
- v_statistic_vn_float
The value of the V-statistic.
- v_statistic_cv_float
The critical value for Vn computed following the asymptotic distribution.
References#
Ding Y., Markatou M., Saraceno G. (2023). “Poisson Kernel-Based Tests for Uniformity on the d-Dimensional Sphere.” Statistica Sinica. doi: doi:10.5705/ss.202022.0347
Examples#
>>> import numpy as np >>> np.random.seed(0) >>> from QuadratiK.poisson_kernel_test import PoissonKernelTest >>> # data generation >>> z = np.random.normal(size=(200, 3)) >>> data_unif = z / np.sqrt(np.sum(z**2, axis=1, keepdims=True)) >>> #performing the uniformity test >>> unif_test = PoissonKernelTest(rho = 0.7, random_state=42).test(data_unif) >>> print("Execution time: {:.3f} seconds".format(unif_test.execution_time)) >>> print("U Statistic Results") >>> print("H0 is rejected : {}".format(unif_test.u_statistic_h0_)) >>> print("Un Statistic : {}".format(unif_test.u_statistic_un_)) >>> print("Critical Value : {}".format(unif_test.u_statistic_cv_)) >>> print("V Statistic Results") >>> print("H0 is rejected : {}".format(unif_test.v_statistic_h0_)) >>> print("Vn Statistic : {}".format(unif_test.v_statistic_vn_)) >>> print("Critical Value : {}".format(unif_test.v_statistic_cv_)) ... Execution time: 1.894 seconds ... U Statistic Results ... H0 is rejected : False ... Un Statistic : 0.5977824645431915 ... Critical Value : 1.6128083124315886 ... V Statistic Results ... H0 is rejected : False ... Vn Statistic : 19.722614852087553 ... Critical Value : 23.229486935225513
Methods
Function to generate descriptive statistics. |
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Summary function generates a table for the poisson kernel test results and the summary statistics. |
Performs the Poisson kernel-based quadratic distance Goodness-of-fit tests for Uniformity for spherical data using the Poisson kernel with concentration parameter \(rho\) |
- PoissonKernelTest.stats()#
Function to generate descriptive statistics.
Returns#
- summary_stats_dfpandas.DataFrame
Dataframe of descriptive statistics
- PoissonKernelTest.summary(print_fmt='simple_grid')#
Summary function generates a table for the poisson kernel test results and the summary statistics.
Parameters#
- print_fmtstr, optional.
Used for printing the output in the desired format. Supports all available options in tabulate, see here: https://pypi.org/project/tabulate/. Defaults to “simple_grid”.
Returns#
- summarystr
A string formatted in the desired output format with the kernel test results and summary statistics.
- PoissonKernelTest.test(x)#
Performs the Poisson kernel-based quadratic distance Goodness-of-fit tests for Uniformity for spherical data using the Poisson kernel with concentration parameter \(rho\)
Parameters#
- xnumpy.ndarray, pandas.DataFrame
a numeric d-dim matrix of data points on the Sphere \(S^{(d-1)}\).
Returns#
- selfobject
Fitted estimator