I am intended to fit the following data using InhomogeneousPoissonProcess[]
in v12.0.
The original form of data tabulated given as below
Such a table contains counts by the hour and day of the week, arriving phone calls associated with a call center which is open from 8 am-9 pm daily, for an example,
Days = ToString /@ {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday};
counts = {{42, 47, 79, 101, 83, 74, 79, 105, 88, 94, 84, 51, 68}, {63,
144, 133, 163, 140, 104, 137, 145, 163, 150, 113, 91, 79}, {75,
129, 148, 144, 134, 128, 132, 135, 150, 119, 102, 66, 58}, {76,
115, 97, 127, 98, 120, 130, 130, 124, 97, 92, 51, 77}, {57, 108,
184, 134, 131, 109, 129, 135, 118, 108, 94, 77, 69}, {72, 134,
139, 129, 123, 114, 106, 156, 145, 123, 102, 67, 68}, {56, 91, 93,
96, 77, 83, 86, 109, 127, 95, 81, 68, 45}}; (*Arrival counts to a call center*)
{995, 1625, 1520, 1334, 1453, 1478, 1107} (*Total per day*)
{441, 768, 873, 894, 786, 732, 799, 915, 915, 786, 668, 471, 464} (*Total per hour*)
Before modeling, I wanted to create a mathematical model (hypothesis test) using, which assumes that the daily arrivals to a call center occur according to the inhomogeneous Poisson process.
I tried to find similar but could find in neither here InhomogeneousPoissonProcess or there Hypothesis Tests guides.
EDIT: My question is, to validate the assumptions of Inhomogeneous PP given such data set. I have not made any set of hypotheses, but only hinted to have a hypothesis based on mean and variance relationship.
Please help me to set up hypothesis tests for NHPP models based on count events using such tools.
Thank you for your time.