Confirmation of Binary Clustering in Gamma-Ray Bursts through an Integrated $p$-value from Multiple Nonparametric Tests of Hypotheses

The paper applies a new, nonparametric, interpoint distance-based measure to confirm the inherent groups prevailing in the brightest source of light in the universe: gamma-ray bursts. Our effective metric, in association with clustering methods like Gaussian-mixture model-based and $K$-means algorithms, resolves the conflict regarding the possibility about existence of more than binary clusters in the gamma-ray burst population. Here we carry out multiple nonparametric statistical tests of hypotheses, as many as the number of bursts available from the `BATSE' catalog. An integrated $p$-value achieved from the aforesaid dependent tests solves our concern confirming two groups of short and long bursts.