Statistics/Chi-squared distribution: Difference between revisions
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(Created Nim solution.) |
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For the airport data, diff total is 4.512820512820512, χ2 is 0.08875392598443503, p value 0.7888504263193064 |
For the airport data, diff total is 4.512820512820512, χ2 is 0.08875392598443503, p value 0.7888504263193064 |
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</pre> |
</pre> |
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=={{header|Nim}}== |
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{{libheader|gnuplotlib.nim}} |
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Adapted from Python solution. |
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<syntaxhighlight lang="Nim">import std/[math, strformat, sugar] |
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func χ²(x: float; k: int): float = |
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## χ² function, the probability distribution function (pdf) for χ². |
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if x > 0: x.pow(k / 2 - 1) * exp(-x/2) / (2.pow(k / 2) * gamma(k / 2)) else: 0 |
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func gammaCdf(k, x: float): float = |
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## Lower incomplete gamma by series formula with gamma. |
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for m in 0..99: |
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result += x^m / gamma(k + m.toFloat + 1) |
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result *= pow(x, k) * exp(-x) |
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func cdfχ²(x: float; k: int): float = |
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## Cumulative probability function (cdf) for χ². |
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if x > 0 and k > 0: gammaCdf(k / 2, x / 2) else: 0 |
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echo " Values of the χ2 probability distribution function" |
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echo " x/k 1 2 3 4 5" |
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for x in 0..10: |
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stdout.write &"{x:2} " |
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for k in 1..5: |
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stdout.write &"{χ²(x.toFloat, k):10.6f}" |
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echo() |
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echo() |
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echo " Values for χ2 with 3 degrees of freedom" |
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echo "χ² cum pdf p-value" |
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for x in [1, 2, 4, 8, 16, 32]: |
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let cdf = cdfχ²(x.toFloat, 3) |
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echo &"{x:2} {cdf:10.6f} {1 - cdf:10.6f}" |
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const |
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AirportData = [[float 77, 23], [float 88, 12], [float 79, 21], [float 81, 19]] |
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Expected = [[81.25, 18.75], [81.25, 18.75], [81.25, 18.75], [81.25, 18.75]] |
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var dtotal = 0.0 |
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for pos in [0, 1]: |
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for i, d in AirportData: |
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dtotal += (d[pos] - Expected[i][pos])^2 / Expected[i][pos] |
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echo() |
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echo &"For the airport data, diff total is {dtotal:.6f}, " & |
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&"χ² is {χ²(dtotal, 3):.6f}, p value is {cdfχ²(dtotal, 3):.6f}." |
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### Stretch task ### |
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import gnuplot |
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let x = collect(for n in 0..9999: n / 1000) |
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withGnuplot: |
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cmd "set multiplot" |
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cmd "set yrange [-0.02:0.5]" |
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for k in 0..3: |
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let y = collect(for p in x: χ²(p, k)) |
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plot(x, y, &"k = {k}", "with lines") |
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</syntaxhighlight> |
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{{out}} |
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<pre> Values of the χ2 probability distribution function |
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x/k 1 2 3 4 5 |
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0 0.000000 0.000000 0.000000 0.000000 0.000000 |
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1 0.241971 0.303265 0.241971 0.151633 0.080657 |
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2 0.103777 0.183940 0.207554 0.183940 0.138369 |
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3 0.051393 0.111565 0.154180 0.167348 0.154180 |
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4 0.026995 0.067668 0.107982 0.135335 0.143976 |
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5 0.014645 0.041042 0.073225 0.102606 0.122042 |
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6 0.008109 0.024894 0.048652 0.074681 0.097304 |
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7 0.004553 0.015099 0.031873 0.052845 0.074371 |
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8 0.002583 0.009158 0.020667 0.036631 0.055112 |
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9 0.001477 0.005554 0.013296 0.024995 0.039887 |
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10 0.000850 0.003369 0.008500 0.016845 0.028335 |
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Values for χ2 with 3 degrees of freedom |
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χ² cum pdf p-value |
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1 0.198748 0.801252 |
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2 0.427593 0.572407 |
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4 0.738536 0.261464 |
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8 0.953988 0.046012 |
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16 0.998866 0.001134 |
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32 0.999999 0.000001 |
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For the airport data, diff total is 4.512821, χ² is 0.088754, p value is 0.788850. |
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</pre> |
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[[File:Chi-squared-nim.png]] |
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=={{header|Perl}}== |
=={{header|Perl}}== |
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