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            "text": "# Statistics::Distributions (perldoc)\n\n## NAME\n\nStatistics::Distributions - Perl module for calculating critical values and upper probabilities of common statistical distributions\n\n## SYNOPSIS\n\nuse Statistics::Distributions;\n$chis=Statistics::Distributions::chisqrdistr (2,.05);\nprint \"Chi-squared-crit (2 degrees of freedom, 95th percentile \"\n.\"= 0.05 level) = $chis\\n\";\n$u=Statistics::Distributions::udistr (.05);\nprint \"u-crit (95th percentile = 0.05 level) = $u\\n\";\n$t=Statistics::Distributions::tdistr (1,.005);\nprint \"t-crit (1 degree of freedom, 99.5th percentile = 0.005 level) \"\n.\"= $t\\n\";\n$f=Statistics::Distributions::fdistr (1,3,.01);\nprint \"F-crit (1 degree of freedom in numerator, 3 degrees of freedom \"\n.\"in denominator, 99th percentile = 0.01 level) = $f\\n\";\n$uprob=Statistics::Distributions::uprob (-0.85);\nprint \"upper probability of the u distribution (u = -0.85): Q(u) \"\n.\"= 1-G(u) = $uprob\\n\";\n$chisprob=Statistics::Distributions::chisqrprob (3,6.25);\nprint \"upper probability of the chi-square distribution (3 degrees \"\n.\"of freedom, chi-squared = 6.25): Q = 1-G = $chisprob\\n\";\n$tprob=Statistics::Distributions::tprob (3,6.251);\nprint \"upper probability of the t distribution (3 degrees of \"\n.\"freedom, t = 6.251): Q = 1-G = $tprob\\n\";\n$fprob=Statistics::Distributions::fprob (3,5,.625);\nprint \"upper probability of the F distribution (3 degrees of freedom \"\n.\"in numerator, 5 degrees of freedom in denominator, F = 6.25): \"\n.\"Q = 1-G = $fprob\\n\";\n\n## DESCRIPTION\n\nThis Perl module calculates percentage points (5 significant digits) of the u (standard normal)\ndistribution, the student's t distribution, the chi-square distribution and the F distribution.\nIt can also calculate the upper probability (5 significant digits) of the u (standard normal),\nthe chi-square, the t and the F distribution. These critical values are needed to perform\nstatistical tests, like the u test, the t test, the F test and the chi-squared test, and to\ncalculate confidence intervals.\n\n## Sections\n\n- **NAME**\n- **SYNOPSIS**\n- **DESCRIPTION**\n- **BUGS**\n- **INSTALLATION**\n- **AVAILABILITY**\n- **AUTHOR**\n- **COPYRIGHT**\n- **SEE ALSO**\n\nUse structuredContent.sections for detailed options, examples, and full documentation.\n"
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        "summary": "Statistics::Distributions - Perl module for calculating critical values and upper probabilities of common statistical distributions",
        "synopsis": "use Statistics::Distributions;\n$chis=Statistics::Distributions::chisqrdistr (2,.05);\nprint \"Chi-squared-crit (2 degrees of freedom, 95th percentile \"\n.\"= 0.05 level) = $chis\\n\";\n$u=Statistics::Distributions::udistr (.05);\nprint \"u-crit (95th percentile = 0.05 level) = $u\\n\";\n$t=Statistics::Distributions::tdistr (1,.005);\nprint \"t-crit (1 degree of freedom, 99.5th percentile = 0.005 level) \"\n.\"= $t\\n\";\n$f=Statistics::Distributions::fdistr (1,3,.01);\nprint \"F-crit (1 degree of freedom in numerator, 3 degrees of freedom \"\n.\"in denominator, 99th percentile = 0.01 level) = $f\\n\";\n$uprob=Statistics::Distributions::uprob (-0.85);\nprint \"upper probability of the u distribution (u = -0.85): Q(u) \"\n.\"= 1-G(u) = $uprob\\n\";\n$chisprob=Statistics::Distributions::chisqrprob (3,6.25);\nprint \"upper probability of the chi-square distribution (3 degrees \"\n.\"of freedom, chi-squared = 6.25): Q = 1-G = $chisprob\\n\";\n$tprob=Statistics::Distributions::tprob (3,6.251);\nprint \"upper probability of the t distribution (3 degrees of \"\n.\"freedom, t = 6.251): Q = 1-G = $tprob\\n\";\n$fprob=Statistics::Distributions::fprob (3,5,.625);\nprint \"upper probability of the F distribution (3 degrees of freedom \"\n.\"in numerator, 5 degrees of freedom in denominator, F = 6.25): \"\n.\"Q = 1-G = $fprob\\n\";",
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        "see_also": [
            {
                "name": "perl",
                "section": "1",
                "url": "https://www.chedong.com/phpMan.php/man/perl/1/json"
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        "sections": {
            "NAME": {
                "content": "Statistics::Distributions - Perl module for calculating critical values and upper probabilities\nof common statistical distributions\n",
                "subsections": []
            },
            "SYNOPSIS": {
                "content": "use Statistics::Distributions;\n\n$chis=Statistics::Distributions::chisqrdistr (2,.05);\nprint \"Chi-squared-crit (2 degrees of freedom, 95th percentile \"\n.\"= 0.05 level) = $chis\\n\";\n\n$u=Statistics::Distributions::udistr (.05);\nprint \"u-crit (95th percentile = 0.05 level) = $u\\n\";\n\n$t=Statistics::Distributions::tdistr (1,.005);\nprint \"t-crit (1 degree of freedom, 99.5th percentile = 0.005 level) \"\n.\"= $t\\n\";\n\n$f=Statistics::Distributions::fdistr (1,3,.01);\nprint \"F-crit (1 degree of freedom in numerator, 3 degrees of freedom \"\n.\"in denominator, 99th percentile = 0.01 level) = $f\\n\";\n\n$uprob=Statistics::Distributions::uprob (-0.85);\nprint \"upper probability of the u distribution (u = -0.85): Q(u) \"\n.\"= 1-G(u) = $uprob\\n\";\n\n$chisprob=Statistics::Distributions::chisqrprob (3,6.25);\nprint \"upper probability of the chi-square distribution (3 degrees \"\n.\"of freedom, chi-squared = 6.25): Q = 1-G = $chisprob\\n\";\n\n$tprob=Statistics::Distributions::tprob (3,6.251);\nprint \"upper probability of the t distribution (3 degrees of \"\n.\"freedom, t = 6.251): Q = 1-G = $tprob\\n\";\n\n$fprob=Statistics::Distributions::fprob (3,5,.625);\nprint \"upper probability of the F distribution (3 degrees of freedom \"\n.\"in numerator, 5 degrees of freedom in denominator, F = 6.25): \"\n.\"Q = 1-G = $fprob\\n\";\n",
                "subsections": []
            },
            "DESCRIPTION": {
                "content": "This Perl module calculates percentage points (5 significant digits) of the u (standard normal)\ndistribution, the student's t distribution, the chi-square distribution and the F distribution.\nIt can also calculate the upper probability (5 significant digits) of the u (standard normal),\nthe chi-square, the t and the F distribution. These critical values are needed to perform\nstatistical tests, like the u test, the t test, the F test and the chi-squared test, and to\ncalculate confidence intervals.\n\nIf you are interested in more precise algorithms you could look at: StatLib:\nhttp://lib.stat.cmu.edu/apstat/ ; Applied Statistics Algorithms by Griffiths, P. and Hill, I.D.,\nEllis Horwood: Chichester (1985)\n",
                "subsections": []
            },
            "BUGS": {
                "content": "This final version 1.02 has been released after more than one year without a bug report on the\nprevious version 0.07. Nevertheless, if you find any bugs or oddities, please do inform the\nauthor.\n",
                "subsections": []
            },
            "INSTALLATION": {
                "content": "See perlmodinstall for information and options on installing Perl modules.\n",
                "subsections": []
            },
            "AVAILABILITY": {
                "content": "The latest version of this module is available from the Distribution Perl Archive Network\n(CPAN). Please visit http://www.cpan.org/ to find a CPAN site near you or see\nhttp://www.cpan.org/authors/id/M/MI/MIKEK/ .\n",
                "subsections": []
            },
            "AUTHOR": {
                "content": "Michael Kospach <mike.perl@gmx.at>\n\nNice formating, simplification and bug repair by Matthias Trautner Kromann <mtk@id.cbs.dk>\n",
                "subsections": []
            },
            "COPYRIGHT": {
                "content": "Copyright 2003 Michael Kospach. All rights reserved.\n\nThis library is free software; you can redistribute it and/or modify it under the same terms as\nPerl itself.\n",
                "subsections": []
            },
            "SEE ALSO": {
                "content": "Statistics::ChiSquare, Statistics::Table::t, Statistics::Table::F, perl(1).\n",
                "subsections": []
            }
        }
    }
}