Mathematical Statistics with Mathematica

A.  Totes amazeballs automated Plotting

Let random variable X have pdf f(x):


B.  Elegant Piecewise Processing Engine

mathStatica 2.7’s piecewise processing engine provides beautiful support for piecewise functions, with clean and elegant solutions that are streets ahead of anything else available.

For example, here we compare mathStatica 2.7’s elegant output to Mathematica output (by itself), for exactly the same problem ... calculating a cdf:


C.  Even more Distributions

mathStatica, of course, handles infinitely many distributions (univariate or multivariate). For ease and convenience, mathStatica 2.7 adds another 40 univariate distributions to the built-in palettes, offering simple easy one-click access.

Continuous   Discrete
alpha-Laplace distribution (see Linnik distribution)
A cute Linear distribution
Arc-Sine distribution
asymmetric Laplace distribution
Azzalini's skew-Normal distribution
Bates distribution
Beta distribution
Beta distribution of the second kind (see Inverted Beta distribution)
Bi-weight distribution
Birnbaum–Saunders distribution
Box–Tiao distribution (see Subbotin distribution)
Bradford distribution
Burr Type III distribution
Burr Type XII distribution
Cardioid distribution
Cauchy distribution
Chi distribution
Chi-squared distribution
Cosine distribution
Cosinus distribution
Dagum Type I distribution
Double Epanechnikov distribution
Double Exponential distribution (see Laplace distribution)
Double Freud distribution (see Reflected Freud distribution)
Double Gamma distribution (see Reflected Gamma distribution)
Double Weibull distribution (see Reflected Weibull distribution)
Epanechnikov distribution
Exponential distribution
Extreme Value distribution
Fisher's F distribution
folded Normal distribution
Fréchet distribution
Freud distribution
Gamma distribution
Gaussian distribution (see Normal distribution)
Generalised Beta distribution
Generalised Normal distribution (see Subbotin distribution)
Gumbel Type I distribution (see Extreme Value distribution)
Hahn distribution
half-Cauchy distribution
half-Halo distribution
half-Logistic distribution
half-Normal distribution
Hyperbolic Secant distribution
Inverse Chi-squared distribution
Inverse Gamma distribution
Inverse Gaussian distribution
Inverse Triangular distribution
Inverted Beta distribution
Irwin-Hall distribution
Johnson family distributions
Kumaraswamy distribution
Laplace distribution
Leipnik distribution
Levy distribution
Lindley distribution
Linnik distribution
Logistic distribution
Loglogistic distribution
Lognormal distribution
Lomax distribution
Maxwell-Boltzmann distribution
Moyal distribution
noncentral Chi-squared distribution
noncentral F distribution
Normal distribution
Normal two-component-mix distribution
Pareto distribution
Pareto II distribution (see Lomax)
Pearson family distributions
Power Exponential distribution (see Subbotin distribution)
Power Function distribution
Power semi-circle distribution
Quartic distribution (see Bi-weight distribution)
Random Walk distribution
Rayleigh distribution
Rectangular distribution (see Uniform distribution)
Reflected Freud distribution
Reflected Gamma distribution
Reflected Weibull distribution
Rice distribution
scaled Beta distribution
semi-circle distribution
shifted Exponential distribution
Sinc2 distribution
Sine2 distribution
skew-Normal distribution
skew-V distribution
stable distribution
Stacy distribution
STSP (Standard Two-Sided Power) distribution
Student's t distribution
Subbotin distribution
Topp-Leone distribution
Trapezoidal distribution
Tri-cubic distribution
Tri-weight distribution
Triangular distribution
Truncated Normal distribution
U-quadratic distribution
Uniform distribution
V distribution
Wald distribution (see Inverse Gaussian)
Weibull distribution
Z distribution
  Banach distribution
Bernoulli distribution
Beta-Binomial distribution
Beta-Geometric distribution
Binomial distribution
difference of 2 Geometric distribution
DiGamma distribution
discrete Pareto distribution (see Riemann Zeta distribution)
Dubey distribution
Estoup distribution
Fibonacci distribution
Flory distribution
Geometric distribution
Geometric[0, ∞] distribution
Gross-Miller Geometric distribution
Haight's Zeta distribution
Holla distribution
Hunter Geometric distribution
Hypergeometric distribution
Inverse Binomial distribution
Jackson-Nickols distribution
Kelly distribution
Kupper distribution
Lehmann distribution
Logarithmic distribution
Lotka distribution
Miller distribution
Moran-Gani distribution
Naor-Poisson distribution
Negative Binomial distribution
Ord-Geometric distribution (see Two-sided Geometric)
Pascal distribution
Poisson distribution
Poisson two-component-mix distribution
Poisson-Lindley distribution
Polya-Aeppli distribution
Prasad distribution
Rademacher distribution
Rectangular distribution (see Uniform distribution)
Riemann Zeta distribution
Schwarz-Tversky (Type 1) distribution
Schwarz-Tversky (Type 3) distribution
Schwarz-Tversky (Type 4) distribution
Simon distribution
Srinivasan distribution
Takacs distribution
Tambouratzis distribution
Triangular distribution
Triangular of order λ distribution
TriGamma distribution
Two-sided Geometric distribution
Uniform[0,n] distribution (discrete)
Uniform[a,b] distribution (discrete)
Waiting-time Negative Binomial distribution
Waring distribution
Yanagimoto distribution (see Inverse Binomial)
Yule distribution
Zero-Inflated Poisson distribution (ZIP)
Zeta distribution (see Riemann Zeta)
Zipf distribution
Zipf-Mandelbrot distribution

The distribution palettes have also been significantly updated and re-organised, and are now sorted both alphabetically and by domain of support, with appropriate forms for each distribution already set-up for each domain of support, for maximum ease of use.


D.   Parallel Processing Engine

mathStatica 2.7’s parallel processing engine unleashes the power of your computer — automatically — featuring phenomenal speed and power for users with multi-processor machines ...

Timings in seconds using Mathematica 11
running on Mac Pro computer


E.  Help System ... decidedly uber

Click to view


F.   Major New Functions in 2.x
RandomNumber random number generation for essentially any discrete or continuous univariate distribution 




pdf of max(X, Y, Z, ...)   [ Show me ]


TransformProduct pdf of X * Y   [ Show me ]


OrderStatNonIdentical  pdf of order statistics sampling from non-identical parent distributions   [ Show me ]




automated fitting for the Johnson SU and SL family


Non-rectangular domains greatly enhanced support  

Multivariate discrete seamlessly extended to core functions  

Unbiased estimators now all multivariate ...
The entire suite of unbiased estimator functions now support arbitrary multivariate worlds.  

Moments of moments now all multivariate ...
The entire suite of moments of moments functions are now multivariate.

e.g. Find the covariance between, say:
    and   [ Show me ]


G.   Palettes in 2.7
mathStatica supports infinitely many distributions.

In fact, there are so many new distributions in mathStatica 2.7, there isn’t enough space to fit them all on screen. The new continuous and discrete palettes now have a scrolling design that allows us to add unlimited numbers of distributions, and to display them both alphabetically and sorted by domain of support.

Continuous Discrete Book


H.   Easy to use
Simply press the 'Start' button ...

Incredibly easy!


I.   Rose and Smith (latest edition)
Latest book edition!

Takes full advantage of the front-end interface:

  • real-time interactive animations
  • dynamic links
  • compatible with Mma 13
  • single-click to open any section
  • all seamlessly integrated
  • now available with all solutions

Up-to-date electronic Mathematica text!

Single download includes everything!