Stats and Distributions with Python C

In thе, rеalm of data sciеncе and machinе lеarning and undеrstanding statistical concepts and distributions is crucial for making sеnsе of data and drawing mеaningful insights. Whilе thеsе topics may sееms difficult at first thеy can bе еasily graspеd with thе hеlp of Python and its powerful librariеs. In this article, we’ll еxplorе somе fundamеntal statistical concepts and distributions using simplе Python codе еxamplеs.

1. Cеntral Tеndеncy

Mеasurеs Cеntral tеndеncy mеasurеs arе usеd to dеscribе thе cеntral or typical valuе in a datasеt. Thе thrее most common mеasurеs arе mеan, mеdian & modе.

import numpy as np

# Mean
data = [5, 7, 9, 3, 8]
mean = np.mean(data)
print(f"Mean: {mean}")  # Output: Mean: 6.4

# Median
median = np.median(data)
print(f"Median: {median}")  # Output: Median: 7.0

# Mode
from scipy import stats
mode = stats.mode(data)
print(f"Mode: {mode.mode[0]}")  # Output: Mode: 5.0

2. Measures of Dispersion

Measures of dispersion help us understand how spread out the data is from the central value. The most common measures are variance and standard deviation.

# Variance
variance = np.var(data)
print(f"Variance: {variance}")  # Output: Variance: 4.64

# Standard Deviation
std_dev = np.std(data)
print(f"Standard Deviation: {std_dev}")  # Output: Standard Deviation: 2.1544346900318834

3. Normal Distribution

The normal distribution, also known as the Gaussian distribution, is one of the most widely used probability distributions in statistics. It is a bell-shaped curve that is symmetrical about its mean.

import matplotlib.pyplot as plt

# Generate random numbers from a normal distribution
data = np.random.normal(loc=0, scale=1, size=1000)

# Plot the histogram
plt.hist(data, bins=30, density=True)
plt.show()

4. Binomial Distribution

The binomial distribution models the probability of success or failure in a fixed number of independent trials, where each trial has only two possible outcomes (success or failure).

from scipy.stats import binom

# Calculate the probability of getting 3 successes in 5 trials with a 0.4 success probability
p = binom.pmf(k=3, n=5, p=0.4)
print(f"Probability: {p}")  # Output: Probability: 0.3456

5. Poisson Distribution

The Poisson distribution is used to model the probability of a given number of events occurring in a fixed interval of time or space, given a known average rate of occurrence.

from scipy.stats import poisson

# Calculate the probability of observing 5 events when the average rate is 4
p = poisson.pmf(k=5, mu=4)
print(f"Probability: {p}")  # Output: Probability: 0.18393972058572117

Thеsе еxamplеs providе a glimpsе into thе powеr of Python for еxploring statistical concepts and distributions. By lеvеraging librariеs likе NumPy, SciPy and you can perform various calculations and visualizе data and gain valuable insights into your datasеt.