Runs a chi-squared goodness-of-fit test: observed counts (binned at roughly equal-probability quantiles of the fitted Poisson distribution, so expected counts stay adequate regardless of where the data sits) vs. Poisson-expected counts, with one degree of freedom subtracted for the estimated rate. The test is deterministic — no simulated comparison sample is drawn.
Value
A one-row tibble of test results (empty if col isn't
valid count data, e.g. it has negative values).
Details
A Kolmogorov-Smirnov test is deliberately *not* used here: the KS
statistic's null distribution assumes a continuous CDF, and the Poisson
distribution is discrete with real point masses, which inflates the KS
statistic (and deflates its p-value) regardless of true fit — the
chi-squared test is the standard, correctly-calibrated tool for
discrete/count goodness-of-fit. is_normal uses the
Lilliefors variant of the Kolmogorov-Smirnov test, which suits the
continuous normal distribution.
Since the Poisson distribution's support is the non-negative integers, this returns an empty tibble for vectors containing negative values or fewer than 2 observations.
Examples
is_poisson(rpois(n = 1000, lambda = 2))
#> # A tibble: 1 × 8
#> statistic parameter p.value method distribution.test p_value_sig distribution
#> <dbl> <int> <dbl> <chr> <lgl> <chr> <chr>
#> 1 10.2 4 0.0369 Chi-sq… FALSE * poisson
#> # ℹ 1 more variable: is_int <lgl>
is_poisson(runif(1000, min = 2, max = 4))
#> # A tibble: 1 × 8
#> statistic parameter p.value method distribution.test p_value_sig
#> <dbl> <int> <dbl> <chr> <lgl> <chr>
#> 1 760. 4 4.27e-163 Chi-squared test … FALSE ***
#> # ℹ 2 more variables: distribution <chr>, is_int <lgl>