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      _____ _        _   _     _   _          
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     \___ \| __/ _` | __| / __| __| |/ __/ __|
     ____) | || (_| | |_| \__ \ |_| | (__\__ \
    |_____/ \__\__,_|\__|_|___/\__|_|\___|___/v0.0.6

NAME
====

Statistics - Raku module for doing statistics

SYNOPSIS
========

```raku
use Statistics;

my @data1 = [6,6,4,6,8,6,8,4,4,6,6,8,8,8,8,8,8,4,4,4,4,8,8,8,8,4,4,4,8,6,8,4];
my @data2 = [160.0,160.0,108.0,258.0,360.0,225.0,360.0,146.7,140.8,167.6,167.6,
            275.8,275.8,275.8,472.0,460.0,440.0,78.7,75.7,71.1,120.1,318.0,304.0,
            350.0,400.0,79.0,120.3,95.1,351.0,145.0,301.0,121.0];

# central tendency
mean(@data1); # 6.1875
median(@data1); # 6

# sample standard deviation
sd(@data1); # 1.7859216469465444

# population standard deviation
sd(@data1, sample => False); # 1.757795138803154

# Coefficient of variation
coef_variation(@data2); # 53.71779066522493

# Five number summary
fivenum(@data2); # (71.1 120.65 196.3 334 472)

# correlation coefficients
pearson_cor_coef(@data1, @data2); # 0.9020328721469989
spearman_cor_coef(@data1, @data2); # 0.9276515785415314
kendall_cor_coef(@data1, @data2); # 0.8144262510988963

# Biweight_midcorrelation 
# more robust, less sensitive to outliers
bi_cor_coef(@data1, @data2); # 0.9146470012038392

# numpy linspace
linspace(2.1, 3.2, 5, endpoint => False, retstep => False); # [2.1, 2.32, 2.54, 2.76, 2.98]
linspace(1, 3, 3, endpoint => False, retstep => True); # ([1, 1.666667, 2.333333], 0.666667)


# pdf of normal distribution 
raku_dnorm(5); # 1.4867195147342977e-06
raku_dnorm(3, mean => 2, sd => 1); # 0.24197072451914337
raku_dnorm(3, mean => 2, sd => -1); # NaN;
raku_dnorm(3, mean => 2, sd => 0); # 0;

# cdf of normal distribution 
raku_pnorm(5); # 0.9999997133484281
raku_pnorm(4, mean => 2, sd => 3); # 0.7475074624530771
raku_pnorm(4, mean => 2, sd => 3, log_p => True) # -0.29101099055230867


raku_qnorm(5); # NaN


# Random number generator for normal distribution 
set_seed(111,222);
raku_rnorm(12) # (0.2933064931910023 -0.43157564134676835 0.1280404124560668 -1.001461811038476 -0.9219453227924342 1.2988990178409578 -0.46867271131577315 -1.2678609176619775 0.3596981905325252 0.35262105537769173 0.5770092689090144 -1.0392300758070165) 

# Multinomial coefficients
multinomial_coef([3,1,1,3,4.2, 8, 90, 40]); # 2.717246116384229e+69;
multinomial_coef([3,1,1,3,4.2, 8, 90, 140]); # 1.0317825100856673e+106;
multinomial_coef([2,4,5,7]); # 220540320

multinomial_coef_excel([3,1.9,1,3,4.2]); # 554400;
```

DESCRIPTION
===========

Statistics is a module to make it easier to do statistics in Raku programming language.



Features
--------

+ [x] descriptive statistics
+ [x] correlation coefficients
+ [x] pdf, cdf of probability distributions 
+ [x] random number generators
+ [ ] parametric tests
+ [ ] non-parametric tests


### INSTALLATION 

The module contains **compiled** code. `gcc`, `cmake` and `ninja` 
are required for compilation and should be available in `PATH`.

### ISSUES

https://github.com/sumanstats/Statistics/issues

### PULL REQUESTS

Improvement of the code base and efficient implementation of the algorithms are welcome.

AUTHOR
======

Dr Suman Khanal <suman81765@gmail.com>

COPYRIGHT AND LICENSE
=====================

Copyright 2022 Dr Suman Khanal

This library is free software; you can redistribute it and/or modify it under the Artistic License 2.0.