Statistics Category Group

1. CapeTools Statistical Distributions

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   General Description

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   Functions to create Statistical Distribution objects (both Discrete and Continuous). You can either create classical distribution objects or create distribution objects given raw data. The latter distribution objects can then be subject to a variety of hypotheses tests.
   
   The types of classical distributions that can be created are :
   
   

   • Bernoulli
   • Binomial
   • Chi-square
   • Continuous Constant
   • Continuous Uniform
   • Discrete Constant
   • Discrete Uniform
   • Exponential
   • Hypergeometric
   • Normal
   • Lognormal
   • Poisson
   • Rayleigh
   • F
   • Student's T
   • Weibull

   
   
   Once these distribution objects have been created you can create Random Process objects from them and thus generate random numbers. You can additionally query the distribution objects for its properties.
   
   
   
2. CapeTools Query Statistical Distributions

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   General Description

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   Functions to query the properties of a Continuous Statistical Distribution object (ie - mean, variance and standard deviation,).
   
   Functions to generate statistical values of a Continuous Statistical Distribution object (ie - execute the probability density function, cumulative distribution function, inverse cumulative distribution and the hazard function)
   
   Functions to query the properties of a Discrete Statistical Distribution object (ie - mean, variance and standard deviation,).
   
   Functions to generate statistical values of a Discrete Statistical Distribution object (ie - execute the probability function and the cumulative function)
   
   
   
3. CapeTools Statistical Hypothesis Objects

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   General Description

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   Functions to create Hypothesis testing objects given a Generic Continuous Distribution object. A Generic Continuous Distribution object is an object created via the GenericContinuousDist() function and populated with user data. The user now wishes to compare the properties of this generic distribution against the normal distribution.
   
   The types of Hypothesis testing objects that can be created are.
   
   

   • Hypothesis objects for the mean of normal distribution with known sigma.
   • Hypothesis objects for the mean of normal distribution with unknown sigma.
   • Hypothesis objects for the difference between means of two normal distributions with known sigmas (not paired).
   • Hypothesis objects for the difference between means of two normal distributions with unknown sigmas (not paired).
   • Hypothesis objects for the variance of normal distribution.
   • Hypothesis objects for the ratio of two variances (F-Test).

   
   
   
   
   
4. CapeTools Query Statistical Hypothesis Objects

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   General Description

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   Functions to execute a hypothesis test given a Hypothesis testing object.
   
   The types of Hypothesis testing that can be conducted are.
   
   

   • Test for the mean of normal distribution with known sigma.
   • Test for the mean of normal distribution with unknown sigma.
   • Test for the difference between means of two normal distributions with known sigmas (not paired).
   • Test for the difference between means of two normal distributions with unknown sigmas (not paired).
   • Test for the variance of normal distribution.
   • Test for the ratio of two variances (F-Test).

   
   
   Given these testing objects, the functions present here can apply one-sided or two-sided tests. You can retrieve the probability of getting the observed test statistic value as well as the result of the test.
   
   
   
5. CapeTools Statistical Random Process Objects

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   General Description

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   Functions to create Statistical Random Process Object given a Statistical Distribution object. A Statistical Random Process Object generates random numbers. It is important to note that once the object has been created, you set the Reload flag parameter to zero (0). This will prevent the object from being re-created.
   
   
   
6. CapeTools Statistical Random Generators

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   General Description

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   Functions to generate random numbers given a Statistical Random Process Object.