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Statistics usually includes:
statistical distribution: normal distribution, t distribution, gamma distribution, chi-square distribution, F distribution;
statistical modeling: Linear regression, Logistic regression, Generalized linear model, etc;
ANOVA, factor analysis, etc.
Focus on both correlation and causal relation analysis aomong variables and factors.
Using both R and Python to implement statistical programming.
Using ggolot2 in R and matplotlib in Python specially for plotting various statisticl figures.
Normal distribution is describing random variables with bell-shaped probability density functions. Normal distribution is widely used in data science because large sample random variates have a mean value which follows approximate normal distribution if variates are independently drawn from any distributions. The probability density function for normal distribution is determined by two parameters: mean(miu) and standard deviation(sigma).
When a correlation, usually Person type correlation, is calculated, two variables have to be continuous. But this requirement does not excludes the situation when one of the two variables is a dichotomous (binary) distributed. Say if we want to measure the correlations between height and gender for a group of people, the variable gender has clear dichotomous values. This kind of Pearson correlation is called point-biserial correlation, because the value for gender variable is strictly 0 or 1.
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.
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.
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.
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.
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.
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.
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.
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.