por Calculations such as the Bernoulli distribution in Big Data statistics are presented as a great benefit in data processing. In general, statistics are an accurate and necessary way both for a data exploration to guide you through key questions as well as for the analysis and visualization of big data.
For this reason, understanding how these types of strategies are developed will help you in your processing of the data and the results returned. Thus, In this post, we explain everything about Bernoulli’s essay either Bernoulli distribution in Big Data statistics.
What are the types of distributions in statistics?
Before introducing you to what the Bernoulli distribution is used for in Big Data statistics, We want to remind you what they are and what distributions you can find.
The types of distributions in statistics are part of the probability functions that appear most frequently when a statistical study is carried out.
As a summary, these are the types of distributions in Big Data statistics:
Uniform distribution: keep going. The values all have the same possibility.
Bernoulli Distribution: discreet There are two possible solutions to the Bernoulli distribution or Bernoulli probability; For example: flipping a coin.
Exponential Distribution: keep going. The mean time between occurrence of events of a Bernoulli distribution.
Binomial Distribution: discreet Bernoulli generalization. For example: throw several coins in the air.
Poisson distribution: discreet Generalization of Binomial when there are infinite events of very low probability.
Gaussian Distribution: keep going. The most used distribution, any combination of random variables tends to a Gaussian one.
Chi square distribution: keep going. The square of a Gaussian distribution.
Bernoulli distribution in Big Data statistics
The Bernoulli probability or the Bernoulli distribution in Big Data statistics It is a discrete distribution that can take two values: one with probability and one without. Therefore, this is used to describe events that only have two possible outcomes, such as, for example, Yes/No, 1/0 or Heads/Tails.
A clearer example I would be Toss a coin in the air once and wait for which of the two sides comes up when it falls.
On the other hand, the Bernoulli probability or the Bernoulli distribution in Big Data statistics has the following formulas for the mean and variance estimators:
options(repr.plot.height=2,repr.plot.width=6) p<- 0.7 q<- 1–p df <- data.frame(x=c(«Yes»,»No»), try=c(p,q)) ggplot(data=df,aes(x=x,y=prob))+geom_point(color=«blue»)+geom_col(width=0.005,color=«blue»)+
theme_bw()+ggtitle(«Probability density function \n of a Bernoulli distribution») options(repr.plot.height=4,repr.plot.width=6)
The probability density function of the Bernoulli distribution in Big Data statistics can be represented as:
where k It only allows two possible values in the Bernoulli distribution
This formula of Bernoulli essay or Bernoulli distribution can also be expressed as:
The Bernoulli model or Bernoulli distribution in Big Data statistics is a special case of the binomial distribution with n=1. You can simulate a Bernoulli distribution from a uniform one simply comparing whether the value exceeds a threshold that is determined by the probability of the binomial distribution.
p <- 0.1v<-runif(5,min=0,max=1) v as.integer(v>p)
0.860110642388463 0.956164636649191 0.926419156603515 0.0539636595640332 0.246409463929012 1 1 1 0 1
options(repr.plot.height=4,repr.plot.width=6) slices <- c(p,1–p) lbls <- c(«Heads», «Tails») pie(slices, labels = lbls, main=«Probability»)
Now, once you know how the Bernoulli model works either the Bernoulli distribution in Big Data statisticswe familiarize you with the binomial that derives from this:
Binomial distribution from the Bernoulli model
The binomial distribution is a generalization of the Bernoulli distribution for independent eventseach of which has two possible outcomes (Yes/No) with probability.
To do this, you must take into account the variables that define the distribution:
p – the probability of success of an individual case.
n – the number of total events that you want to measure.
k – the number of events in which YES has appeared.
On the other hand, the registration of this type of binomial distribution for the mean and variance estimators is this:
How to learn more about Big Data?
In this post, we have exposed you everything related to the Bernoulli distribution in Big Data statistics. Now, remember that you must take into account Why do other distributions work within statistics in the management of big data?so that you can effectively decide which of them is the best for your study.
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