Data Science different topic's explanation -- Part-11 -- Poisson Distribution

[anish-arya]

This is data science different topic explanation conversation series.
If you are not following below mentioned are the links for each part.

Part-1:

Data Science different explanation -- An introduction

Data Science different explanation – An introduction [image] There are a lot of engineers who have never been involved in the field of statistics or Data Science. But in order to build data pipelines or rewrite produced code by Data Scientists to an adequate, easily maintained code many nuances and misunderstandings arise on the engineering side. For those Data/ML engineers and novice Data Scientists, I’ve made this series of posts. I will try to explain some basic approaches in plain eng…

Part-2:

Data Science different topic explanation -- Part-2 -- Events. Probabilities of events

If you missed the previous post, here’s the below mentioned link. Data Science different topic explanation – Part-2 – Events. Probabilities of events One of the basic concepts in statistics in an event. Events are simply results of experiments. Events can be certain impossible, or random. A certain event is an event that as a result of an experiment (the execution of certain actions with a certain set of conditions) will occur in 100% cases. For instance, tossed coin will certainly fall (on…

Part-3:

Data Science different topic explanation -- Part-3 -- Event Types

This is Data Science different topic explanation conversation series. If you are not following this conversation series below are the link: Part-1: Part-2: Data Science different topic explanation – Part-3 – Event Types Independent and Dependent events Two random events A and B are called independent if the occurrence of one of them does not change the probability of the occurrence of the other. Otherwise, events A and B are called dependent. Counterintuitively, knowing that the coin l…

Part-4:

Data Science different topic explanation -- Part-4 -- Disjoint and overlapping events

This is data science different topic explanation conversation series. If you are not following below mentioned are the links for each part. Part-1: Part-2: Part-3: Data Science different topic explanation – Part-4 – Disjoint and overlapping events Disjoint events cannot happen at the same time. A synonym for this term is “mutually exclusive”. For instance, the outcome of a single coin toss cannot be head and a tail, it can be either head or tails. The not disjoint event can happend a…

Part-5:

Data Science different topic's explanation -- Part-5 -- Types of Probabilities

This is data science different topic explanation conversation series. If you are not following below mentioned are the links for each part. Part-1: Part-2: Part-3: Part-4: Data Science different topic’s explanation – Part-5 – Types of Probabilities Joint Probability Joint probability is a type of probability where more than one event can occur simultaneously. The joint probability is the probability that event A will occur at the same time as event B. For instance, from a deck o…

Part-6:

Data Science different topic's explanation -- Part-6 -- Marginal Probability and Conditional Probability

This is data science different topic explanation conversation series. If you are not following below mentioned are the links for each part. Part-1: Part-2: Part-3: Part-4: Part-5: Data Science different topic’s explanation – Part-6 – Marginal Probability and Conditional Probability Marginal Probability Marginal Probability – a probability of any single event occurring unconditioned on any other events. Whenever someone asks you whether the weather is going to be rainy or sunny t…

Part-7:

Data Science different topic's explanation -- Part-7 -- Probability Distributions

Continuing the conversation series for next topic here. Cumulative Distribution Function (CDF) The cumulative distribution function provides an integral picture of the probability distribution. As the name cumulative suggests, it is simply the probability that a variable will take a value less than or equal to particular value. In the example above given x=3, the CDF tells us the sum probability of all random variables form 1 to 3.

Part-8:

Data Science different topic's explanation -- Part-8 -- Continuous distributions

This is data science different topic explanation conversation series. If you are not following below mentioned are the links for each part. Part-1: Part-2: Part-3: Part-4: Part-5: Part-6: Part-7: Continuous distributions We investigate probabilistic distributions of continuous random variables, i.e. random variables whose support contains an infinite range of possible outcomes. Uniform Distribution A uniform distribution is a type of distribution of probabilities where all …

Part-9:

Data Science different topic's explanation -- Part-9 -- Normal Distribution

This is data science different topic explanation conversation series. If you are not following below mentioned are the links for each part. Part-1: Part-2: Part-3: Part-4: Part-5: Part-6: Part-7: Part-8: Data Science different topic’s explanation – Part-9 – Normal Distribution from scipy.stats import norm import matplotlib.pyplot as plt import numpy as np def normal() -> None: fig, ax = plt.subplots(1, 1) # calculate a few first moments mean, var, skew, kurt = n…

Part-10:

Data Science different topic's explanation -- Part-10 -- Discrete distributions

This is data science different topic explanation conversation series. If you are not following below mentioned are the links for each part. Part-1: Part-2: Part-3: Part-4: Part-5: Part-6: Part-7: Part-8: Part-9: Data Science different topic’s explanation – Part-10 – Discrete distributions Bernoulli distribution (binomial distribution) from scipy.stats import bernoulli import seaborn as sb def bernoulli_dist(): -> None: data_bern = bernoulli.rvs(size=1000,p=0.6) a…

Data Science different topic’s explanation – Part-11 – Poisson Distribution

from scipy.stats import poisson
import seaborn as sb
import numpy as np
import matplotlib.pyplot as plt


def poisson_dist(): -> None
    plt.figure(figsize=(15,15))
    data_binom = poisson.rvs(mu=4, size=10000)

    ax = sb.distplot(data_binom, kde=True, color='b', 
                    bins=np.arange(data_binom.min(), data_binom.max() + 1), 
                    kde_kws={'color': 'r', 'lw': 3, 'label': 'KDE'})
    ax.set(xlabel='Poisson', ylabel='Frequency')

poisson_dist()

The Poisson distribution is obtained as a limiting case of the Bernoulli distribution, if we push p to zero and n to infinity, but so that their product remains constant: n * p - a. Formally, such transition leads to the formula

• x is a random variable (the number of occurrences of event A);
• λ is the event rate (average number of events in an interval) so called the rate parameter. It is also equal to mean and variance.

[anish-arya]

Continuing the missed out content.

Poisson’s distribution is subject to many random variables that arise in scientific and practical life: equipment breaks, the duration of maintenance work performed by working staff, printing errors, the number of goals scored by the football team.

In closing

There are many theoretical distributions: Normal, Poisson, Student, Fisher, Binomial and others. Each of them is intended for analysis of data of different origin and has certain characteristics. In practice these distributions are used as some template for analysis of real data of similar type. In other words, they try to impose the structure of the chosen theoretical distribution on real data, thus calculating the characteristics that are of interest to the analyst.

[anish-arya]

More precisely, theoretical distributions are probabilistic statistical models whose properties are used to analyse empirical data. Something like that is done. Data are collected and compared to any known theoretical distributions. If there are similarities, the properties of a theoretical model are transmitted to the empirical data with the corresponding conclusions. This approach is the basis for classical methods related to the hypotheses testing (calculation of confidence intervals, comparison of mean values, verification of parameters’ significance, etc.).

[anish-arya]

If the available data do not correspond to any known theoretical distribution (which usually happens in practice, but for some reason, nobody cares), it is not recommended to use the selected template (probabilistic-statistical model). Illegal use of parametric distributions leads to the situation when an analyst searches for keys not where he has lost them, but under a street lamp pole where it is light. To solve this problem, there are other approaches related to using non-parametric statistics.