R Programming
Using t-distribution and t-test with R
A Student t-distributed random variable is modeling the ratio between a standard Normal random variate and square root of a Chi-squared random variable divided by its degrees of freedom.
ggplot2
Kernel density plots with ggplot2 in R
Kernel density function is a nonparametric method to find the drawing density curve of random samples, and it is often used to draw a smoothed curve in data visualization. In R programming with ggplot2 package, a chaining of functions ggplot() and geom_density() is often used to draw different smoothed curves showing the distribution of continuous variables.
Python
Using a function with a while loop in Python
A function in Python is a group of code statements wrapped together to perform specific tasks. After a function is defined, then it can be called by passing real values to its arguments and get the returning results. A while loop in Python is a group of conditional statements bundled in a statement beginning with keyword ‘while’, and the codes will run forever until the condition returns false. By including a user-defined function inside a while loop in Python, many iterative tasks can be fulfilled.
Python
Poisson distribution implementation in Python
Poisson distribution is a discrete distribution. It is frequently used to model the counts of event occurrence during a specified time interval, such as telephone calls coming in to a call center in a given day. There is one parameter in the Poisson probability function, λ, which denotes the constant occurring rate in a Poisson process.
Python
Calculating Type I Error and Type II Error in Hypothesis Testing using Python
In hypothesis testing, the possibility of the other side than the conclusion usually exists, and the analysis commits so-called Type I and Type II errors, with respect to the truth and the decision made upon the random sample and hypotheses. In particular, a Type I error measures the probability that a true Null hypothesis (H0) is incorrectly rejected, and a Type II error says the probability that a false H0 not being rejected, respectively.
R Programming
Calculating The Power of a Test in Hypothesis Testing with R
In hypothesis testing, the analyst has chance to commit both Type I and Type II errors. The Type I error (α) refers to the probability of wrongly rejecting a true Null hypothesis – H0, while the Type II error (ß) represents the probability that failing to reject a false H0. The value of 1- ß is called the Power of Test in hypothesis testing. Its value says the ability of correctly rejecting a false H0, under the specified Null hypothesis – H0 and Alternative hypothesis – H1.
R Programming
Calculating Type I Error and Type II Error of Hypothesis Testing using R
In statistical hypothesis testing, there are usually two types of errors that the process will encounter, namely Type I and type II errors. Type I error (α) refers to the probability of rejection of a Null Hypothesis (H0) when actually it is true, and if a false Null hypothesis is missed to reject when an Alternative Hypothesis (H1) is true, then a type II error (ß) occurs.
R Programming
Using Weibull distribution in R programming
Weibull distribution, named after Swedish mathematician Waloddi Weibull, is a continuous distribution which is widely used to model the distribution of random time between events. Exponential distribution, which is used to model the random time until next event occurs and have so-called memoryless feature or constant failure rate. In order to relax this memoryless condition, analysts may use either Gamma distribution or Weibull distribution instead.
R Programming
Using Lognormal distributions in R programming
Lognormal distribution in probability and statistics is used to model the distribution of a positive random variable Y, if Y = ln(X) has a normal distribution with mean μ and standard deviation σ.
R Programming
Implementing beta distribution in R programming
Beta distribution is a family of distributions which are used to model the probability of continuous random variables defined on [0, 1]. There are two parameters , α and β in Beta distribution. A continuous uniform distribution defined on [0, 1] is actually a special case of a beta distribution, when both α and β equal 1.