from os.path import basename, exists


def download(url):
    filename = basename(url)
    if not exists(filename):
        from urllib.request import urlretrieve

        local, _ = urlretrieve(url, filename)
        print("Downloaded " + local)


download("https://github.com/AllenDowney/ThinkStats2/raw/master/code/thinkstats2.py")
download("https://github.com/AllenDowney/ThinkStats2/raw/master/code/thinkplot.py")

import numpy as np

import thinkstats2
import thinkplot

"""
Explanation: Chapter 5
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
"""


thinkplot.PrePlot(3)
for lam in [2.0, 1, 0.5]:
    xs, ps = thinkstats2.RenderExpoCdf(lam, 0, 3.0, 50)
    label = r"$\lambda=%g$" % lam
    thinkplot.Plot(xs, ps, label=label)

thinkplot.Config(title="Exponential CDF", xlabel="x", ylabel="CDF", loc="lower right")

"""
Explanation: Exponential distribution
Here's what the exponential CDF looks like with a range of parameters.
End of explanation
"""


download("https://github.com/AllenDowney/ThinkStats2/raw/master/code/nsfg.py")
download("https://github.com/AllenDowney/ThinkStats2/raw/master/code/analytic.py")
download("https://github.com/AllenDowney/ThinkStats2/raw/master/code/babyboom.dat")

import analytic

df = analytic.ReadBabyBoom()
diffs = df.minutes.diff()
cdf = thinkstats2.Cdf(diffs, label="actual")

thinkplot.Cdf(cdf)
thinkplot.Config(xlabel="Time between births (minutes)", ylabel="CDF")

"""
Explanation: Here's the distribution of interarrival times from a dataset of birth times.
End of explanation
"""


thinkplot.Cdf(cdf, complement=True)
thinkplot.Config(
    xlabel="Time between births (minutes)",
    ylabel="CCDF",
    yscale="log",
    loc="upper right",
)

"""
Explanation: Here's what the CCDF looks like on a log-y scale.  A straight line is consistent with an exponential distribution.
End of explanation
"""


thinkplot.PrePlot(3)

mus = [1.0, 2.0, 3.0]
sigmas = [0.5, 0.4, 0.3]
for mu, sigma in zip(mus, sigmas):
    xs, ps = thinkstats2.RenderNormalCdf(mu=mu, sigma=sigma, low=-1.0, high=4.0)
    label = r"$\mu=%g$, $\sigma=%g$" % (mu, sigma)
    thinkplot.Plot(xs, ps, label=label)

thinkplot.Config(title="Normal CDF", xlabel="x", ylabel="CDF", loc="upper left")

"""
Explanation: Normal distribution
Here's what the normal CDF looks like with a range of parameters.
End of explanation
"""


download("https://github.com/AllenDowney/ThinkStats2/raw/master/code/nsfg.py")
download("https://github.com/AllenDowney/ThinkStats2/raw/master/code/first.py")
download("https://github.com/AllenDowney/ThinkStats2/raw/master/code/2002FemPreg.dct")
download(
    "https://github.com/AllenDowney/ThinkStats2/raw/master/code/2002FemPreg.dat.gz"
)

import nsfg
import first

preg = nsfg.ReadFemPreg()
weights = preg.totalwgt_lb.dropna()

"""
Explanation: I'll use a normal model to fit the distribution of birth weights from the NSFG.
End of explanation
"""


# estimate parameters: trimming outliers yields a better fit
mu, var = thinkstats2.TrimmedMeanVar(weights, p=0.01)
print("Mean, Var", mu, var)

# plot the model
sigma = np.sqrt(var)
print("Sigma", sigma)
xs, ps = thinkstats2.RenderNormalCdf(mu, sigma, low=0, high=12.5)

thinkplot.Plot(xs, ps, label="model", color="0.6")

# plot the data
cdf = thinkstats2.Cdf(weights, label="data")

thinkplot.PrePlot(1)
thinkplot.Cdf(cdf)
thinkplot.Config(title="Birth weights", xlabel="Birth weight (pounds)", ylabel="CDF")

"""
Explanation: Here's the observed CDF and the model.  The model fits the data well except in the left tail.
End of explanation
"""


n = 1000
thinkplot.PrePlot(3)

mus = [0, 1, 5]
sigmas = [1, 1, 2]

for mu, sigma in zip(mus, sigmas):
    sample = np.random.normal(mu, sigma, n)
    xs, ys = thinkstats2.NormalProbability(sample)
    label = "$\mu=%d$, $\sigma=%d$" % (mu, sigma)
    thinkplot.Plot(xs, ys, label=label)

thinkplot.Config(
    title="Normal probability plot",
    xlabel="standard normal sample",
    ylabel="sample values",
)

"""
Explanation: A normal probability plot is a visual test for normality.  The following example shows that if the data are actually from a normal distribution, the plot is approximately straight.
End of explanation
"""


mean, var = thinkstats2.TrimmedMeanVar(weights, p=0.01)
std = np.sqrt(var)

xs = [-4, 4]
fxs, fys = thinkstats2.FitLine(xs, mean, std)
thinkplot.Plot(fxs, fys, linewidth=4, color="0.8")

xs, ys = thinkstats2.NormalProbability(weights)
thinkplot.Plot(xs, ys, label="all live")

thinkplot.Config(
    title="Normal probability plot",
    xlabel="Standard deviations from mean",
    ylabel="Birth weight (lbs)",
)

"""
Explanation: Here's the normal probability plot for birth weights, showing that the lightest babies are lighter than we expect from the normal mode, and the heaviest babies are heavier.
End of explanation
"""


full_term = preg[preg.prglngth >= 37]
term_weights = full_term.totalwgt_lb.dropna()

"""
Explanation: If we suspect that the deviation in the left tail is due to preterm babies, we can check by selecting only full term births.
End of explanation
"""


mean, var = thinkstats2.TrimmedMeanVar(weights, p=0.01)
std = np.sqrt(var)

xs = [-4, 4]
fxs, fys = thinkstats2.FitLine(xs, mean, std)
thinkplot.Plot(fxs, fys, linewidth=4, color="0.8")

thinkplot.PrePlot(2)
xs, ys = thinkstats2.NormalProbability(weights)
thinkplot.Plot(xs, ys, label="all live")

xs, ys = thinkstats2.NormalProbability(term_weights)
thinkplot.Plot(xs, ys, label="full term")
thinkplot.Config(
    title="Normal probability plot",
    xlabel="Standard deviations from mean",
    ylabel="Birth weight (lbs)",
)

"""
Explanation: Now the deviation in the left tail is almost gone, but the heaviest babies are still heavy.
End of explanation
"""


download("https://github.com/AllenDowney/ThinkStats2/raw/master/code/brfss.py")
download("https://github.com/AllenDowney/ThinkStats2/raw/master/code/CDBRFS08.ASC.gz")

import brfss

df = brfss.ReadBrfss()
weights = df.wtkg2.dropna()

"""
Explanation: Lognormal model
As an example of a lognormal disrtribution, we'll look at adult weights from the BRFSS.
End of explanation
"""


def MakeNormalModel(weights):
    """Plots a CDF with a Normal model.

    weights: sequence
    """
    cdf = thinkstats2.Cdf(weights, label="weights")

    mean, var = thinkstats2.TrimmedMeanVar(weights)
    std = np.sqrt(var)
    print("n, mean, std", len(weights), mean, std)

    xmin = mean - 4 * std
    xmax = mean + 4 * std

    xs, ps = thinkstats2.RenderNormalCdf(mean, std, xmin, xmax)
    thinkplot.Plot(xs, ps, label="model", linewidth=4, color="0.8")
    thinkplot.Cdf(cdf)

"""
Explanation: The following function estimates the parameters of a normal distribution and plots the data and a normal model.
End of explanation
"""


MakeNormalModel(weights)
thinkplot.Config(
    title="Adult weight, linear scale",
    xlabel="Weight (kg)",
    ylabel="CDF",
    loc="upper right",
)

"""
Explanation: Here's the distribution of adult weights and a normal model, which is not a very good fit.
End of explanation
"""


log_weights = np.log10(weights)
MakeNormalModel(log_weights)
thinkplot.Config(
    title="Adult weight, log scale",
    xlabel="Weight (log10 kg)",
    ylabel="CDF",
    loc="upper right",
)

"""
Explanation: Here's the distribution of adult weight and a lognormal model, plotted on a log-x scale.  The model is a better fit for the data, although the heaviest people are heavier than the model expects.
End of explanation
"""


def MakeNormalPlot(weights):
    """Generates a normal probability plot of birth weights.

    weights: sequence
    """
    mean, var = thinkstats2.TrimmedMeanVar(weights, p=0.01)
    std = np.sqrt(var)

    xs = [-5, 5]
    xs, ys = thinkstats2.FitLine(xs, mean, std)
    thinkplot.Plot(xs, ys, color="0.8", label="model")

    xs, ys = thinkstats2.NormalProbability(weights)
    thinkplot.Plot(xs, ys, label="weights")

"""
Explanation: The following function generates a normal probability plot.
End of explanation
"""


MakeNormalPlot(weights)
thinkplot.Config(
    title="Adult weight, normal plot",
    xlabel="Weight (kg)",
    ylabel="CDF",
    loc="upper left",
)

"""
Explanation: When we generate a normal probability plot with adult weights, we can see clearly that the data deviate from the model systematically.
End of explanation
"""


MakeNormalPlot(log_weights)
thinkplot.Config(
    title="Adult weight, lognormal plot",
    xlabel="Weight (log10 kg)",
    ylabel="CDF",
    loc="upper left",
)

"""
Explanation: If we make a normal probability plot with log weights, the model fit the data well except in the tails, where the heaviest people exceed expectations.
End of explanation
"""


xmin = 0.5

thinkplot.PrePlot(3)
for alpha in [2.0, 1.0, 0.5]:
    xs, ps = thinkstats2.RenderParetoCdf(xmin, alpha, 0, 10.0, n=100)
    thinkplot.Plot(xs, ps, label=r"$\alpha=%g$" % alpha)

thinkplot.Config(title="Pareto CDF", xlabel="x", ylabel="CDF", loc="lower right")

"""
Explanation: Pareto distribution
Here's what the Pareto CDF looks like with a range of parameters.
End of explanation
"""


download("https://github.com/AllenDowney/ThinkStats2/raw/master/code/populations.py")
download("https://github.com/AllenDowney/ThinkStats2/raw/master/code/PEP_2012_PEPANNRES_with_ann.csv")

import populations

pops = populations.ReadData()
print("Number of cities/towns", len(pops))

"""
Explanation: The distribution of populations for cities and towns is sometimes said to be Pareto-like.
End of explanation
"""


log_pops = np.log10(pops)
cdf = thinkstats2.Cdf(pops, label="data")
cdf_log = thinkstats2.Cdf(log_pops, label="data")

# pareto plot
xs, ys = thinkstats2.RenderParetoCdf(xmin=5000, alpha=1.4, low=0, high=1e7)
thinkplot.Plot(np.log10(xs), 1 - ys, label="model", color="0.8")

thinkplot.Cdf(cdf_log, complement=True)
thinkplot.Config(
    xlabel="log10 population", ylabel="CCDF", yscale="log", loc="lower left"
)

"""
Explanation: Here's the distribution of population for cities and towns in the U.S., along with a Pareto model.  The model fits the data well in the tail.
End of explanation
"""


thinkplot.PrePlot(cols=2)

mu, sigma = log_pops.mean(), log_pops.std()
xs, ps = thinkstats2.RenderNormalCdf(mu, sigma, low=0, high=8)
thinkplot.Plot(xs, ps, label="model", color="0.8")

thinkplot.Cdf(cdf_log)
thinkplot.Config(xlabel="log10 population", ylabel="CDF", loc="lower right")

"""
Explanation: The lognormal model might be a better fit for this data (as is often the case for things that are supposed to be Pareto).
End of explanation
"""


thinkstats2.NormalProbabilityPlot(log_pops, label="data")
thinkplot.Config(xlabel="Random variate", ylabel="log10 population", xlim=[-5, 5])

"""
Explanation: Here's a normal probability plot for the log-populations.  The model fits the data well except in the right tail, where the biggest cities are bigger than expected.
End of explanation
"""


import random


def expovariate(lam):
    p = random.random()
    x = -np.log(1 - p) / lam
    return x

"""
Explanation: Random variates
When we have an analytic CDF, we can sometimes invert it to generate random values.  The following function generates values from an exponential distribution.
End of explanation
"""


t = [expovariate(lam=2) for _ in range(1000)]

"""
Explanation: We can test it by generating a sample.
End of explanation
"""


cdf = thinkstats2.Cdf(t)

thinkplot.Cdf(cdf, complement=True)
thinkplot.Config(xlabel="Exponential variate", ylabel="CCDF", yscale="log")

"""
Explanation: And plotting the CCDF on a log-y scale.
End of explanation
"""


# Solution


def sample_pareto(alpha, x_m, size):
    u = np.random.random(size)
    return x_m * pow(1 - u, -1 / alpha)

# Solution

sample = sample_pareto(1, 2, 1000)
cdf = thinkstats2.Cdf(sample)

thinkplot.Cdf(cdf, complement=True)
thinkplot.Config(xlabel="Random values", ylabel="CCDF", xscale="log", yscale="log")

"""
Explanation: A straight line is consistent with an exponential distribution.
Exercises
Exercise: Write a function that generates a Pareto variate. Generate a sample and plot its complementary CDF on a log-log scale. Does it look like a straight line?
End of explanation
"""


import scipy.stats

"""
Explanation: Exercise: In the BRFSS (see Section 5.4), the distribution of heights is roughly normal with parameters µ = 178 cm and σ = 7.7 cm for men, and µ = 163 cm and σ = 7.3 cm for women.
In order to join Blue Man Group, you have to be male between 5’10” and 6’1” (see http://bluemancasting.com). What percentage of the U.S. male population is in this range? Hint: use scipy.stats.norm.cdf.
scipy.stats contains objects that represent analytic distributions
End of explanation
"""


mu = 178
sigma = 7.7
dist = scipy.stats.norm(loc=mu, scale=sigma)
type(dist)

"""
Explanation: For example <tt>scipy.stats.norm</tt> represents a normal distribution.
End of explanation
"""


dist.mean(), dist.std()

"""
Explanation: A "frozen random variable" can compute its mean and standard deviation.
End of explanation
"""


dist.cdf(mu - sigma)

"""
Explanation: It can also evaluate its CDF.  How many people are below the mean by more than one standard deviation?  About 16%
End of explanation
"""


# Solution

low = dist.cdf(177.8)  # 5'10"
high = dist.cdf(185.4)  # 6'1"
low, high, high - low

"""
Explanation: How many people are between 5'10" and 6'1"?
End of explanation
"""


alpha = 1.7
xmin = 1  # meter
dist = scipy.stats.pareto(b=alpha, scale=xmin)
dist.median()

"""
Explanation: Exercise: To get a feel for the Pareto distribution, let’s see how different the world would be if the distribution of human height were Pareto. With the parameters xm = 1 m and α = 1.7, we get a distribution with a reasonable minimum, 1 m, and median, 1.5 m.
Plot this distribution. What is the mean human height in Pareto world? What fraction of the population is shorter than the mean? If there are 7 billion people in Pareto world, how many do we expect to be taller than 1 km? How tall do we expect the tallest person to be?
scipy.stats.pareto represents a pareto distribution.  In Pareto world, the distribution of human heights has parameters alpha=1.7 and xmin=1 meter.  So the shortest person is 100 cm and the median is 150.
End of explanation
"""


# Solution

dist.mean()

"""
Explanation: What is the mean height in Pareto world?
End of explanation
"""


# Solution

dist.cdf(dist.mean())

"""
Explanation: What fraction of people are shorter than the mean?
End of explanation
"""


# Solution

(1 - dist.cdf(1000)) * 7e9, dist.sf(1000) * 7e9

"""
Explanation: Out of 7 billion people, how many do we expect to be taller than 1 km?  You could use <tt>dist.cdf</tt> or <tt>dist.sf</tt>.
End of explanation
"""


# Solution

# One way to solve this is to search for a height that we
# expect one person out of 7 billion to exceed.

# It comes in at roughly 600 kilometers.

dist.sf(600000) * 7e9

# Solution

# Another way is to use `ppf`, which evaluates the "percent point function", which
# is the inverse CDF.  So we can compute the height in meters that corresponds to
# the probability (1 - 1/7e9).

dist.ppf(1 - 1 / 7e9)

"""
Explanation: How tall do we expect the tallest person to be?
End of explanation
"""


sample = [random.weibullvariate(2, 1) for _ in range(1000)]
cdf = thinkstats2.Cdf(sample)
thinkplot.Cdf(cdf, transform="weibull")
thinkplot.Config(xlabel="Weibull variate", ylabel="CCDF")

"""
Explanation: Exercise: The Weibull distribution is a generalization of the exponential distribution that comes up in failure analysis (see http://wikipedia.org/wiki/Weibull_distribution). Its CDF is
$\mathrm{CDF}(x) = 1 − \exp[−(x / λ)^k]$ 
Can you find a transformation that makes a Weibull distribution look like a straight line? What do the slope and intercept of the line indicate?
Use random.weibullvariate to generate a sample from a Weibull distribution and use it to test your transformation.
Generate a sample from a Weibull distribution and plot it using a transform that makes a Weibull distribution look like a straight line.
If you are stuck, you can get a hint from thinkplot.Cdf, which provides a transform that makes the CDF of a Weibull distribution look like a straight line.  Here's an example that shows how it's used.
End of explanation
"""


import analytic

df = analytic.ReadBabyBoom()
diffs = df.minutes.diff()
cdf = thinkstats2.Cdf(diffs, label="actual")

n = len(diffs)
lam = 44.0 / 24 / 60
sample = [random.expovariate(lam) for _ in range(n)]

1 / lam, np.mean(sample)

# Solution

model = thinkstats2.Cdf(sample, label='model')
    
thinkplot.PrePlot(2)
thinkplot.Cdfs([cdf, model], complement=True)
thinkplot.Config(xlabel='Time between births (minutes)',
                ylabel='CCDF',
                yscale='log')


# Solution

# If you plot distributions for a large number of samples, you get a sense
# of how much random variation to expect.  In this case, the data fall within
# the range we expect, so there is no compelling reason to think it is
# not exponential.

for i in range(100):
    sample = [random.expovariate(lam) for _ in range(n)]
    thinkplot.Cdf(thinkstats2.Cdf(sample), complement=True, color="0.9")

thinkplot.Cdf(cdf, complement=True)
thinkplot.Config(xlabel="Time between births (minutes)", ylabel="CCDF", yscale="log")

"""
Explanation: Exercise: For small values of n, we don’t expect an empirical distribution to fit an analytic distribution exactly. One way to evaluate the quality of fit is to generate a sample from an analytic distribution and see how well it matches the data.
For example, in Section 5.1 we plotted the distribution of time between births and saw that it is approximately exponential. But the distribution is based on only 44 data points. To see whether the data might have come from an exponential distribution, generate 44 values from an exponential distribution with the same mean as the data, about 33 minutes between births.
Plot the distribution of the random values and compare it to the actual distribution. You can use random.expovariate to generate the values.
End of explanation
"""


download("https://github.com/AllenDowney/ThinkStats2/raw/master/code/hinc.py")
download("https://github.com/AllenDowney/ThinkStats2/raw/master/code/hinc06.csv")

import hinc

df = hinc.ReadData()
df

"""
Explanation: Bonus Example: The distributions of wealth and income are sometimes modeled using lognormal and Pareto distributions. To see which is better, let’s look at some data.
The Current Population Survey (CPS) is a joint effort of the Bureau of Labor Statistics and the Census Bureau to study income and related variables. Data collected in 2013 is available from http://www.census.gov/hhes/www/cpstables/032013/hhinc/toc.htm. I downloaded hinc06.xls, which is an Excel spreadsheet with information about household income, and converted it to hinc06.csv, a CSV file you will find in the repository for this book. You will also find hinc.py, which reads this file.
Extract the distribution of incomes from this dataset. Are any of the analytic distributions in this chapter a good model of the data?
End of explanation
"""


xs, ps = df.income.values, df.ps.values
cdf = thinkstats2.Cdf(xs, ps, label="data")
cdf_log = thinkstats2.Cdf(np.log10(xs), ps, label="data")

# linear plot
thinkplot.Cdf(cdf)
thinkplot.Config(xlabel="household income", ylabel="CDF")

"""
Explanation: Here's what the CDF looks like on a linear scale.
End of explanation
"""


xs, ys = thinkstats2.RenderParetoCdf(xmin=55000, alpha=2.5, low=0, high=250000)

thinkplot.Plot(xs, 1 - ys, label="model", color="0.8")

thinkplot.Cdf(cdf, complement=True)
thinkplot.Config(
    xlabel="log10 household income",
    ylabel="CCDF",
    xscale="log",
    yscale="log",
    loc="lower left",
)

"""
Explanation: To check whether a Pareto model describes the data well, I plot the CCDF on a log-log scale.
I found parameters for the Pareto model that match the tail of the distribution.
End of explanation
"""


median = cdf_log.Percentile(50)
iqr = cdf_log.Percentile(75) - cdf_log.Percentile(25)
std = iqr / 1.349

# choose std to match the upper tail
std = 0.35
print(median, std)

"""
Explanation: For the lognormal model I estimate mu and sigma using percentile-based statistics (median and IQR).
End of explanation
"""


xs, ps = thinkstats2.RenderNormalCdf(median, std, low=3.5, high=5.5)
thinkplot.Plot(xs, ps, label="model", color="0.8")

thinkplot.Cdf(cdf_log)
thinkplot.Config(xlabel="log10 household income", ylabel="CDF")

"""
Explanation: Here's what the distribution, and fitted model, look like on a log-x scale.
End of explanation
"""


