To present the application, it offers three main areas:

• Distribution tool
• Statistical tests
• Descriptives

Distribution tool

The distribution tool offers the following features: plot the pdf/pmf, properties (like mean value, variance, and support), cumulative probability, point mass/density, quantiles, and generating/sampling from the distribution. The probability distributions supported are:

Discrete probability distributions:

• Binomial
• Hypergeometric
• Negative binomial (or Pascal as it is also called)
• Poisson
• Zipf

Continuous probability distributions:

• Beta
• Cauchy
• Chi^2 (Chi squarred)
• Exponential
• F (or Fisher-Snedecor as it is also called)
• Gamma
• Normal (or Gaussian as it is also called)
• Student's t
• Weibull

Statistical tests

At the moment, the following tests are supported:

• One way ANOVA (i.e. univariate)
• Chi^2 tests: Pearson's Chi^2 test for independence and observed vs expected counts
• Two sample Student's t-tests: both homoscedastic and heteroscedastic are supported

Descriptives

The following descriptive statistics about an entered dataset are given:

• Number of observations
• Min
• Max
• Mean
• Standard deviation
• Variance
• Median
• Skewness
• Kurtosis

Comments

Please do not hesitate to express you thought about the application. Also, ideas for further functionality are warmly welcome! And donations to support the continuous development are highly appreciated (donations can be made by using the box in the upper right corner of this page)!

General:

• Icon changed
• Decimal separator always "." no matter the chosen locale of the phone (for consistency purposes)
• Screen rotate issues fixed

Distribution tool:

• Typing error: Continuous distributions density output changed from "F([input]) = ..." to "f([input]) = ..."
• Error description at the parameter tab if the parameters are illegal when trying to plot
• Descriptives gets calculated automatically when sampling data
• The link under properties has been made clickable

The aim of the project is to develop an Android-application with basic statistical tools (I really miss R on my phone, but the project won't be a R-clone nevertheless). So far the codename for the application is Statistical Toolbox for Android (or simply STA).

It is not going to be a programming language such as S, but an easy-to-use graphical statistical toolbox. The features I've thought about including in the first version are:

• Quantiles (and fractiles) for a wide range of univariate probability distributions
• Descriptive statistics (the first two or three empirical moments, correlation measures)
• A guide for choosing the right statistical test

The features for the later versions could be:

• Loading datasets (from mail, files on SD-card, or manual input)
• A range of statistical tests

If any of you have any comments, please do not hesitate to submit a comment here or by mail (use the contact form accessible from the top menu or by sending an e-mail to the reverse of mikl.dk @ scienco ).

Let . Because of how the scaled inverse chi-square distribution is defined, it's possible to simulate from it in R as follows (checking the arguments is not included in the following code):

rinvchisq <- function(n, df, scale)
{
  return(scale * (1 / rchisq(n, df)))
}

When we're able to simulate from the distribution, we're able to find quantiles. But we can actually find those directly by using the definition of quantiles and the chi-squared distribution. Assume that we want to find the $\alpha$-quantile $x_\alpha$. Notice that with informal notation, the following holds:

If , then is the -quantile for . All together we now have:

Because of this, we can implement the following in R (checking the arguments is still not included in the following code):

qinvchisq <- function(p, df, scale)
{
  return(scale / qchisq(1 - p, df))
}

Checking the functions can be done like this:

invchisqcheck <- function(p, n, df, scale)
{
  cat("Check of rinvchisq and qinvchisq...\n")
  cat("Quantiles:", p, "\n")
  cat("Simulated with rinvchisq:\n")
  cat(quantile(rinvchisq(simulations, df, scale), quantiles), "\n")
  cat("Calculated with qinvchisq:\n")
  cat(qinvchisq(quantiles, df, scale), "\n")
}

invchisqcheck(c(0.025, 0.975), 100000, 10, 1)
invchisqcheck(c(0.025, 0.975), 100000, 11, 68)

For further information, please refer to http://en.wikipedia.org/wiki/Scale-inverse-chi-square_distribution.