from __future__ import print_function, division

%matplotlib inline

import numpy as np

import nsfg
import first
import thinkstats2
import thinkplot

"""
Explanation: Examples and Exercises from Think Stats, 2nd Edition
http://thinkstats2.com
Copyright 2016 Allen B. Downey
MIT License: https://opensource.org/licenses/MIT
End of explanation
"""


live, firsts, others = first.MakeFrames()

"""
Explanation: Examples
One more time, I'll load the data from the NSFG.
End of explanation
"""


first_wgt = firsts.totalwgt_lb
first_wgt_dropna = first_wgt.dropna()
print('Firsts', len(first_wgt), len(first_wgt_dropna))
 
other_wgt = others.totalwgt_lb
other_wgt_dropna = other_wgt.dropna()
print('Others', len(other_wgt), len(other_wgt_dropna))

first_pmf = thinkstats2.Pmf(first_wgt_dropna, label='first')
other_pmf = thinkstats2.Pmf(other_wgt_dropna, label='other')

"""
Explanation: And compute the distribution of birth weight for first babies and others.
End of explanation
"""


width = 0.4 / 16

# plot PMFs of birth weights for first babies and others
thinkplot.PrePlot(2)
thinkplot.Hist(first_pmf, align='right', width=width)
thinkplot.Hist(other_pmf, align='left', width=width)
thinkplot.Config(xlabel='Weight (pounds)', ylabel='PMF')

"""
Explanation: We can plot the PMFs on the same scale, but it is hard to see if there is a difference.
End of explanation
"""


def PercentileRank(scores, your_score):
    count = 0
    for score in scores:
        if score <= your_score:
            count += 1

    percentile_rank = 100.0 * count / len(scores)
    return percentile_rank

"""
Explanation: PercentileRank computes the fraction of scores less than or equal to your_score.
End of explanation
"""


t = [55, 66, 77, 88, 99]

"""
Explanation: If this is the list of scores.
End of explanation
"""


PercentileRank(t, 88)

"""
Explanation: And you got the 88, your percentile rank is 80.
End of explanation
"""


def Percentile(scores, percentile_rank):
    scores.sort()
    for score in scores:
        if PercentileRank(scores, score) >= percentile_rank:
            return score

"""
Explanation: Percentile takes a percentile rank and computes the corresponding percentile.
End of explanation
"""


Percentile(t, 50)

"""
Explanation: The median is the 50th percentile, which is 77.
End of explanation
"""


def Percentile2(scores, percentile_rank):
    scores.sort()
    index = percentile_rank * (len(scores)-1) // 100
    return scores[index]

"""
Explanation: Here's a more efficient way to compute percentiles.
End of explanation
"""


Percentile2(t, 50)

"""
Explanation: Let's hope we get the same answer.
End of explanation
"""


def EvalCdf(sample, x):
    count = 0.0
    for value in sample:
        if value <= x:
            count += 1

    prob = count / len(sample)
    return prob

"""
Explanation: The Cumulative Distribution Function (CDF) is almost the same as PercentileRank.  The only difference is that the result is 0-1 instead of 0-100.
End of explanation
"""


t = [1, 2, 2, 3, 5]

"""
Explanation: In this list
End of explanation
"""


EvalCdf(t, 0), EvalCdf(t, 1), EvalCdf(t, 2), EvalCdf(t, 3), EvalCdf(t, 4), EvalCdf(t, 5)

"""
Explanation: We can evaluate the CDF for various values:
End of explanation
"""


cdf = thinkstats2.Cdf(live.prglngth, label='prglngth')
thinkplot.Cdf(cdf)
thinkplot.Config(xlabel='Pregnancy length (weeks)', ylabel='CDF', loc='upper left')

"""
Explanation: Here's an example using real data, the distribution of pregnancy length for live births.
End of explanation
"""


cdf.Prob(41)

"""
Explanation: Cdf provides Prob, which evaluates the CDF; that is, it computes the fraction of values less than or equal to the given value.  For example, 94% of pregnancy lengths are less than or equal to 41.
End of explanation
"""


cdf.Value(0.5)

"""
Explanation: Value evaluates the inverse CDF; given a fraction, it computes the corresponding value.  For example, the median is the value that corresponds to 0.5.
End of explanation
"""


first_cdf = thinkstats2.Cdf(firsts.totalwgt_lb, label='first')
other_cdf = thinkstats2.Cdf(others.totalwgt_lb, label='other')

thinkplot.PrePlot(2)
thinkplot.Cdfs([first_cdf, other_cdf])
thinkplot.Config(xlabel='Weight (pounds)', ylabel='CDF')

"""
Explanation: In general, CDFs are a good way to visualize distributions.  They are not as noisy as PMFs, and if you plot several CDFs on the same axes, any differences between them are apparent.
End of explanation
"""


weights = live.totalwgt_lb
live_cdf = thinkstats2.Cdf(weights, label='live')

"""
Explanation: In this example, we can see that first babies are slightly, but consistently, lighter than others.
We can use the CDF of birth weight to compute percentile-based statistics.
End of explanation
"""


median = live_cdf.Percentile(50)
median

"""
Explanation: Again, the median is the 50th percentile.
End of explanation
"""


iqr = (live_cdf.Percentile(25), live_cdf.Percentile(75))
iqr

"""
Explanation: The interquartile range is the interval from the 25th to 75th percentile.
End of explanation
"""


live_cdf.PercentileRank(10.2)

"""
Explanation: We can use the CDF to look up the percentile rank of a particular value.  For example, my second daughter was 10.2 pounds at birth, which is near the 99th percentile.
End of explanation
"""


sample = np.random.choice(weights, 100, replace=True)
ranks = [live_cdf.PercentileRank(x) for x in sample]

"""
Explanation: If we draw a random sample from the observed weights and map each weigh to its percentile rank.
End of explanation
"""


rank_cdf = thinkstats2.Cdf(ranks)
thinkplot.Cdf(rank_cdf)
thinkplot.Config(xlabel='Percentile rank', ylabel='CDF')

"""
Explanation: The resulting list of ranks should be approximately uniform from 0-1.
End of explanation
"""


resample = live_cdf.Sample(1000)
thinkplot.Cdf(live_cdf)
thinkplot.Cdf(thinkstats2.Cdf(resample, label='resample'))
thinkplot.Config(xlabel='Birth weight (pounds)', ylabel='CDF')

"""
Explanation: That observation is the basis of Cdf.Sample, which generates a random sample from a Cdf.  Here's an example.
End of explanation
"""


# Solution goes here
cdf.PercentileRank(7.5)

# Solution goes here
other_cdf.PercentileRank(7.5)

"""
Explanation: This confirms that the random sample has the same distribution as the original data.
Exercises
Exercise: How much did you weigh at birth? If you don’t know, call your mother or someone else who knows. Using the NSFG data (all live births), compute the distribution of birth weights and use it to find your percentile rank. If you were a first baby, find your percentile rank in the distribution for first babies. Otherwise use the distribution for others. If you are in the 90th percentile or higher, call your mother back and apologize.
End of explanation
"""


# Solution goes here
paul = np.random.random(1000)
pk2 = thinkstats2.Pmf(paul)
thinkplot.Pmf(pk2)

# Solution goes here
pk3 = thinkstats2.Cdf(paul)
thinkplot.Cdf(pk3)

# Solution goes here

"""
Explanation: Exercise: The numbers generated by numpy.random.random are supposed to be uniform between 0 and 1; that is, every value in the range should have the same probability.
Generate 1000 numbers from numpy.random.random and plot their PMF.  What goes wrong?
Now plot the CDF. Is the distribution uniform?
End of explanation
"""


