kirpa Shanker Tiwari

There are multiple method to check data distribution
1.       Histogram
Histogram shows data visualization of a variable using bars. It present frequency per value of dataset. If bell shape curve is there we can say data follows normal distribution.
 

In above figure first histogram looks normally distributed and second one looks uniformly distributed.
 
2.       Box plot
Box Plot is technique can be used to identify data type from samples. The Box Plot plots five variable: min, max, median, 1st & 3rd Quantiles. if at both sides of rectangle width is almost equal we can say data is normally distributed

In the figure first plot has outliers and belongs to non –normal data with outliers and second (bottom) graph can be considered normally distributed.
 
3.       QQ plot
QQ plots need more understanding, QQ means Quantile vs quantile, and here we are plotting theoretical vs actual quantiles for variables, this graph is better than box plot to visualize deviation from normal distribution. Uniform distribution has many observation in both extreme however normal plot follow a straight line.
 
4.       Kolmogorov Smirnov test
Kolmogorov Smirnov test calculate the difference between the empirical distribution and the theoretical distribution and defines the test statistic based on those differences. This test can evaluate all type of distribution.
 
5.       Lilliefors test
This test is based on the above test. Here it is accepted that the mean and variance of the population distribution are estimated rather than pre-specified by the user. if p value is > 0.05 we assume normal distribution else non normal.
 
6.       Shapiro Wilk test
This test is the wonderful test and highly used when testing for a normal distribution. It has been developed specifically for the normal distribution and it cannot be used for testing against other distributions. if p value is > 0.05 we assume normal distribution else non normal
7.       Anderson darling Method: This test also use widely along with Shapiro Wilk test and similarly used for detecting normal distribution. if p value is > 0.05 we assume normal distribution else non normal