Are trade arrivals Poisson? Goodness of fit with an estimated rate

Question

Over 100 minutes you bucket the number of trades per minute into categories \{0, 1, 2, 3, \ge 4\} and observe counts [22, 34, 25, 13, 6]. Test whether trade arrivals are Poisson. Set up the statistic and, in particular, get the degrees of freedom right.

Accepted Answer

Estimate the rate. The Poisson mean is not given, so estimate it from the data: total trades \approx 0(22) + 1(34) + 2(25) + 3(13) + 4(6) = 147 over 100 minutes, so \hat\lambda \approx 1.5. Expected counts. Poisson(1.5) probabilities are P(0) = e^{-1.5} = 0.223, P(1) = 1.5\,e^{-1.5} = 0.335, P(2) = \frac{1.5^2}{2}e^{-1.5} = 0.251, P(3) = \frac{1.5^3}{6}e^{-1.5} = 0.126, and P(\ge 4) = 1 - 	ext{those} = 0.066. Times 100: expected [22.3, 33.5, 25.1, 12.6, 6.6]. Statistic. \chi^2 = \frac{(22-22.3)^2}{22.3} + \frac{(34-33.5)^2}{33.5} + \frac{(25-25.1)^2}{25.1} + \frac{(13-12.6)^2}{12.6} + \frac{…

Are trade arrivals Poisson? Goodness of fit with an estimated rate

Your answer

More Statistics questions