Description
This suite consists of four packages: Statistics, Discrete Probability,
Standard Probability Distributions and Hypothesis
Testing which offer the following functionality.
Statistics Module
The Statistics module incorporates evaluation procedures of standard
quantitative measures of centrality (mean) and dispersion of (discrete)
numerical sets. This module incorporates
weighted averages, geometric mean, Inter-Quartile range, mean and standard
deviation, sample variance and the coefficient of variation.
Discrete Probability Module
The Discrete Probability module encapsulates the foundations of discrete
probability and discrete probability distributions. This component includes
the addition law, conditional probability, cumulative distribution function,
mean and variance of a distribution, expected values, covariance and
simplification of expressions involving random variables.
Standard Probability Distributions Module
This module assists in the development of server-side applications that incorporate
the Binomial, Poisson, Normal, Lognormal and Pareto probability distributions. The probability
function, density function, mean, variance, and cumulative distribution functions are implemented
where appropriate and/or their approximations for each distribution.
Confidence Intervals and Hypothesis Testing Module
Within this component we present two aspects of inferential statistics known as confidence intervals and hypothesis
testing. Confidence intervals determine the level of confidence in pointwise statistics (e.g. mean, variance) of the sample
in relation to the statistics for the entire population. With hypothesis testing the user can judge which of several hypotheses
sampled evidence best supports.
Product Details
This suite consists of four modules with the following features:
Statistics Module
- Measures of Mean
- Arithmetic Mean - a measure of centrality for quantitative data
- Median - the middle value when the observations are arranged
in order of magnitude
- Mode - the most frequently occurring observation
- Weighted Average - the arithmetic average of a weighted set
- Geometric Mean - the nth root of the product of all numerical
observations
- Range - the difference between the largest and the smallest
observation
- Measures of Dispersion
- Inter-Quartile Range (IRQ) - a measure of dispersion which is
not affected by extreme values
- Mean Deviation - the sum of the distances between the
observation and the arithmetic mean
- Sample Variance - the sum of the squares of the distances
between the observations and the
arithmetic mean
- Sample Standard Deviation - the measure of dispersion which
has the same units as the observations
and is the square root of the sample variance
- Coefficient of Variation - computes the spread of sets for
observations which have been made in
different units
- Data Presentation
- Frequency Tables - show the number of the elements inside
some intervals
- Cumulative Frequency Tables - show the number of the elements
within a data set either the highest
value (or above the lowest value) of the present frequency table.
- Relative Frequency Tables - help to compare two or more data
sets, normalized the frequencies
Discrete Probability Module
- Discrete Probability
- Discrete probability - a priori and relative frequency definition
- The Addition Law - used when combining event set or testing for their independence
- Conditional probability - the probability of an event assume that another event takes place
- Complementary event probability - the probability of a set of events not taking place
- Discrete Probability Distributions
- Cumulative distribution function - the sum of the probabilities of a sequence of events
- Mean - the sum of the product of the probability of an event with its value
- Variance - a measure of the distributions spread from the mean
- Expected values - the expected value of the random variable
- Covariance - the covariance of two random variables
- Ro - the population correlation coefficient of two random variables
- Expression with random variables and basic probability laws
- Simplify expression - simplify expressions involving the mean, variance, expected values
and covariance of random variables
- Union and Intersection - the basic formulae for calculating the union and the
intersection of two or many events
Standard Probability Distributions Module
- Discrete Random Variables
- The binomial distribution - this is the probability of an experiment to deliver
x `successes' out of n trials
- The Poisson distribution - this is an exponential dependent distribution, especially used in case of rare events
- Continuous Random Variables
- The normal distribution - the bell-shaped symmetrical curve, whose probability is calculated using numerical integration methods
- The Log Normal distribution - the Lognormal distribution is useful for modeling investment returns and the distribution of insurance claim sizes
- The Pareto Distribution - The Pareto distribution is useful for modeling the distribution of insurance claims when we wish
to be cautious in assessing the probability of large claims
- Numerical Methods
- Extended Trapezoidal Rule - this method is implemented in order to evaluate the non-analytic
probability density functions of the Normal and Lognormal distributions
Hypothesis Testing Module
- Normal Confidence Interval - used when large samples with
>30 elements are considered
- Two-sided confidence interval for the mean, proportions, difference between means and difference between proportions
- One-sided confidence interval for the mean, proportions and difference between means
- Estimating the sample size for a given confidence of the mean
- Estimating the sample size for a given confidence of the proportions
- Student Confidence Interval - used when small samples with
<=30 elements are considered
- Two-sided confidence interval for the mean and the difference between means
- One-sided confidence interval for the mean
- Normal Hypothesis Testing - used when large samples with
>30 elements are considered
- Two-sided hypothesis testing for the mean, proportions, difference between means and difference between proportions
- One-sided hypothesis testing for the mean, proportions, difference between means and difference between proportions
- Student Hypothesis Testing - used when small samples with
<=30 elements are considered
- Two-sided hypothesis testing for the mean, proportions and the difference between means
- One-sided confidence interval for the mean, proportions and difference between means
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