STATISTICAL CALCULATOR

Functionalities

• Module 1: Descriptive Analysis
• Module 2: Predictive Analysis
• Module 3: Probability Analysis
• Module 4: Discrete Distribution functions
• Module 5: Continuous Distribution Function
• Module 6: Sample Distribution Test Statistics
• Module 7: Interval Estimation
• Module 8: Non Parametric Analysis
• Module 9: Visualization

Prerequisites

Need to install this library:

:libraries qcc : QUALITY CONTROL CHARTS, library is used fot pareto.chart() matlib : this library is used for integration function

Assumptions

• Different Analysis are performed only for ungrouped data.
• We have defined only central and absolute moment.
• For mode, we are considering only unimodal data.

User Defined Functions and their Local variables

descriptive_analysis() : function to perform these functions

• calculate_mean(data) : calculates mean of data(vector taken from user)

:data_len :length of the data entered data : the data entered by user(as vector) total : summation of Xi's

• cal_median(data) : calculates median of data(vector taken from user)

:variables: data :sorted data data_len :length of the user entered data median_element :first median if data is even no. of length median_element2 :second median if data is even no. of length median_avg :median average of two medians

• mode(data) : calculates mode of data(vector taken from user)

unique_data : unique values in the data count : contains the count of each unique element index : index of element with Maximum count mode_value : return the mode of the data

• variance(data) : calculates variance of data(vector taken from user)

data_len : length of the data total : sum of square of Xi's answer : calculation of variance

• standard_dev(data) : calculates standard deviation of data(vector taken from user)

return square root of variance

• mean_absolute_dev(data) : calculates mean absolute deviation of data(vector taken from user)

sorted : sorted data data_len : length of the data madev : mean absolute value of the data

• cal_range(data) : calculates range of data(vector taken from user)

sorted : sorted data range_data: return range of the data

• cal_quartiles(data) : calculates quartiles of data(vector taken from user)

data_len :length of the user entered data sorted :sorted data quartile :vector that contain all three quartiles

• cal_IQR(data) : calculates inter quartile range of data(vector taken from user)

• minimum(data) : calculates minimum of data(vector taken from user)

sorted : sorted data return first element of sorted data

• maximum(data) : calculates maximum of data(vector taken from user)

sorted : sorted data return last element of sorted data

• cal_skewness(data) : calculates skewness of data(vector taken from user)

quartile :three quartiles of the data skewness_data :Skewness of the data

• cal_kurtosis(data) : calculates kurtosis of data(vector taken from user)

using moments kurtosis is calculated AND ALSO TELL YOU ABOUT THE TYPE OF DATA YOU ENTERED Mesokurtic data Platykurtic data Leptokurtic data

• moments(data) : calculates moments of data(vector taken from user)

CENTRAL MOMENT AND ARBITRARY MOMENTS BOTH

predictive_analysis() : function to perform these 2 functions:

1.Correlation 2.Multiple Regression

• correlation(X,Y) : function returns correlation coefficient between 2 data X and Y where X and Y are taken as user input vetors

• multiple_regression(x1,x2,Y) : function returns coefficient matrix

And regression model is given in function predictive_analysis() x1, x2 and Y are user input vectors CALCULATING R-SQUARED VALUE FOR MULTIPLE REGRESSION

probability_analysis() : function to perform these functions-

1.Permutation 2.combination 3.Basic Probability 4.Conditional Probability 5.Bayes Theorem

• permutation(n,r) : calculates and returns permutation from user input n and r

• combination(n,r) : calculates and returns combination from user input n and r

• basic_probability(favourable,total) : calculates and returns basic probability from user input favourable and total

• conditional_prob(setA,setB) : calculates and returns conditional probability from user input vector setA and setB

• bayes(prob_Ai,B_condAi,n) : calculates and returns value from bayes's theorem

Input parameters: prob_Ai : input vector having probability of Ai B_condAi : input vector B|Ai probaility n : for which probability is desired

discrete_distribution() : function to perform these functions:

1.Uniform 2.Bernoulli 3.Binomial 4.Geometric 5.Hyper Geometric 6. Negative Binomial 7.Poisson 8. Multinomial 9. Multivariate Hypergeometric

• discrete_uniform_Dist(N) : function returns probability distribution function of discrete uniform distribution having N no. of elements as input

• discrete_bernoulli_dist(x,p) : function returns

probability of success p for x=1 probability of faliure 1-p for x=0 and 0 for invalid x where x & p are user inputs

• discrete_binomial_dist(x,n,p) : function returns binomial distribution value for x,n and p user inputs

• discrete_Geometric_Dist(x,p) : function returns geometric distribution for x and p user inputs

• discrete_HyperGeometric_Dist(N,M,n,x) : function returns hyper geometric distribution for N,M,n and x user inputs

• discrete_NegativeBinomial_Dist(x,r,p) : function returns negatve binomial distribution for x, r and p user inputs

• discrete_Poisson_Dist(x,lambda,t) : function returns poisson distribution for x, lambda and t user inputs

• discrete_Multinomial_Dist(n,p) : function returns multinomial distribution for n and p vector user inputs

• discrete_Multivariate_Hypergeometric_Dist(M,x) : function returns Multivariate Hypergeometric distribution for M and x vector user inputs

cont_distribution : this function will call the following functions and take the input---

• Uniform Distribution function : Calculate the probability of random variable following uniform distribution

uniform(a,b,c,d) c and d are the lower and upper limits of integration respectively

• Normal Distribution function : Calculate the probability of random variable following normal distribution

normal_integration(Pop_mean,Pop_var,lower,upper) pop_mean: population mean Pop_var : population variance lower and upper are the lower and upper limits of integration respectively

• Gamma Distribution function : Calculate the probability of random variable following gamma distribution

gamma_dist_integrate(g,lower,upper) g : this variable represent shape parameter lower and upper are the lower and upper limits of integration respectively

• Exponential Distribution function : Calculate the probability of random variable following exponential distribution

prob_expo(Mean,0,RV) mean : mean of the data RV : random variable 0 :is the lower limit

test_statistic() : function to perform these functions-

1. CHI-SQUARE 2. STUDENT T TEST 3.F-TEST 4.Z-TEST

• chi_square(sam,sd_pop,alpha) : function calculates chi square value from parameters given by user It compares calculated chi sqaure value from value from table And returns 0 (to signify null hypothesis is rejected) or returns 1 (to signify null hypothesis is accepted

:Input parameters: sam : sample vector from user sd_pop : standard deviation of population given by user alpha : level of significance

• student_tTest(sam,pop_mean,alpha) : function calculates t value from parameters given by user It compares calculated t value from value from table And returns 0 (to signify null hypothesis is rejected) or returns 1 (to signify null hypothesis is accepted

:Input parameters: sam : sample vector from user pop_mean : mean of population given by user alpha : level of significance

• F_test(sam1,sam2,alpha) : function calculates f value from parameters given by user It compares calculated f value from value from ta ble And prints whether variances are equal or are not equal

:Input parameters: sam1 : sample vector from user sam2 : sample vector from user alpha : level of significance

• z_test(data,mew,sigma,alpha) : function calculates z value from parameters given by user It compares calculated z value from value from ta ble And returns 0 (to signify null hypothesis is rejected) or returns 1 (to signify null hypothesis is accepted

Input parameters: data : data vector from user mew : population mean value from user sigma : standard deviation value from user alpha : level of significance

Interval_estimation : this function will call the following functions and take the input---

• Estimation of Mean : Calculate the interval for population mean for confidence interval (1-alpha)*100 estimation_of_mean(n,s_mean,variance,alpha)

:n : number of elements in the data(n>30) :s_mean : sample mean :variance : sample variance :alpha:level of significance

• estimation_of_mean_T(n,s_mean,variance,alpha)

:n : number of elements in the data(n<30) :s_mean : mean of the data :variance : variance of population :alpha :level of significance

• Estimation of mean difference : Calculate the interval for difference of population mean for confidence interval (1-alpha)*100 estimation_of_mean_difference(n1,n2,X1,X2,variance1,variance2,alpha)

:n1 : number of elements in the first data(n>30) :X1 : first sample mean :variance1 : first sample variance :n2 : number of elements in the first data(n>30) :X2 : second sample mean :variance2 : second sample variance :alpha:level of significance

*estimation_of_mean_difference_T(n1,n2,X1,X2,variance1,variance2,alpha)

:n1 : number of elements in the first data(n<30) :X1 : first mean :variance1 : first population variance :n2 : number of elements in the first data(n<30) :X2 : second mean :variance2 : second population variance :alpha:level of significance

• Estimation of proportion : Calculate the interval for proportion for confidence interval (1-alpha)*100

estimation_of_proportion(n,theta,alpha) :n: number of elements in the data :theta: proportion :alpha:level of significance

• Estimation of proportion difference : Calculate the interval for difference of proportion for confidence interval (1-alpha)*100

estimation_of_proportion_diff(n1,theta1,n2,theta2,alpha) :n1: number of elements in the first data :theta1: first proportion :alpha:level of significance :n2: number of elements in the second data :theta2:second proportion

• Estimation of variance : Calculate the interval for population variance for confidence interval (1-alpha)*100

estimation_of_variance(n,variance,alpha) :n: number of elements in the data :variance: variance of data :alpha:level of significance

• Estimation of variance difference : Calculate the interval for population mean for confidence interval (1-alpha)*100

estimation_of_Ratiovariance(n1,variance1,n2,variance2,alpha) :n1: number of elements in the first data : variance1: variance of first data
:alpha:level of significance :n2: number of elements in the second data :variance2: variance of second data

non_parametric() : function to perform these functions-

1.SIGN TEST 2.WILCOXON SIGNED RANK TEST 3.MANN-WHITNEY TEST 4.KRUSKAL WALLIS TEST

• signTest(med,set,alpha) : function returns 0 (to signify null hypothesis is rejected) or returns 1 (Null hypotheses is accepted)

           : Input parameters:
              mew : taken from user
              set : vector taken from user
              alpha : level of significance
  

• wilcoxon_srt(mew,set,reln,alpha) : function returns 0 (to signify null hypothesis is rejected) or returns 1 (Null hypotheses is accepted)

          :Input parameters:
           mew : taken from user
           set : vector taken from user
           reln : takes values 1,2,3 from user and signifies:
           1 : mew not equal mew_not
           2 : mew > mew_not
           3 : mew < mew_not
           alpha : level of significance

• Mann_whitney_test(x,y,reln,alpha) : function returns 0 (to signify null hypothesis is rejected) or returns 1 (Null hypotheses is accepted)

         :Input parameters:
         	 x : set x taken from user
         	 y : vector taken from user
         	 reln : takes values 1,2,3 from user and signifies:
           1 : mew not equal mew_not
           2 : mew > mew_not
           3 : mew < mew_not
           alpha : level of significance
  

• Kruskal_wallis_test(x,y,z,alpha) : function returns 0 (to signify null hypothesis is rejected) or returns 1 (Null hypotheses is accepted)

    :Input parameters:
        	 x : set x vector taken from user
         	y : set y vector taken from user
         	z : set z vector taken from user
     	alpha : level of significance

> hist() : We can create histograms with the function hist(x) where x is a numeric vector of values to be plotted.

• plot() : It is used to make graphs according to the type of the object passed.The plot() function in R is used to create the line graph.

• lines() : Draws a line in the plot section.

• barplot() : Bar graph can be created in R using the barplot() function.

• pie() : In R the pie chart is created using the pie() function which takes positive numbers as a vector input.

• boxplot() : A Boxplot is an exploratory graphic that allows you to summarize the features of quantitative variables for one or several levels of a discrete variable. In R, it is done by using boxplot().

• qqplot() : A Q-Q plot is a scatterplot created by plotting two sets of quantiles against one another. If both sets of quantiles came from the same distribution, we should see the points forming a line that’s roughly straight.It is done by qqplot()

• qqnorm() : QQ plot normality is defined by qqnorm()

• qqline() : QQ line plot a line using least square distance from scatter points.

• stem() : Stem and Leaf plot, is a special table where each numeric value is split into a stem (First digit(s) ) and a leaf (last Digit).

• pareto.chart() : A Pareto Chart is a sorted bar chart that displays the frequency (or count) of occurrences that fall in different categories, from greatest frequency on the left to least frequency on the right, with an overlaid line chart that plots the cumulative percentage of occurrences.This operation is achieved by pareto.chart() in r.