Monday, 20 May 2013

More screenshots

Below are screenshots of each of the five segments that constitute the portrait mode Scientific Calculator. Note that the inverse operator to a particular function occurs in the same segment as that function.

The first ("Trig") segment comprises the usual trigonometric functions, as well as the square root and square. You can select between degrees or radians by simply pressing the deg/rad button on the bottom row, second left.

iOS App SciStatCalc screenshot - Display of first segment - scientific calculator, trigonometric functions, square, square-root

The second ("Hyp") segment contains the hyperbolic functions, as well as the cube root and cube.

iOS App SciStatCalc screenshot - Second segment of scientific calculator - hyperbolic functions, cube, cube root

The "Log" segment contains the logarithm and power functions, as well as the $_nP_r$ (permutation) and $_nC_r$ (combination) functions, where
$_nP_r=\frac{n!}{(n-r)!}$ i.e. choose r elements from a set of n elements, where ordering is taken into account,
$_nC_r=\frac{n!}{(n-r)!r!}$ i.e. choose r elements from a set of n elements, where ordering is not taken into account

iOS App SciStatCalc screenshot Third segment of scientific calculator - natural logarithm, base-10 logarithm, power functions , n choose r function (combination, permutation )

The fourth segment ("Stat") contains the
  1. Gamma function $\Gamma(x)$, where $\Gamma(x)=\int_0^{\infty}t^{(x-1)}e^{-t}dt$
  2. Lower normalised incomplete Gamma function, $P(a,x)=\frac{1}{\Gamma(a)}\int_0^xt^{a-1}e^{-t}dt$
  3. Upper normalised incomplete Gamma function $Q(a,x)=\frac{1}{\Gamma(a)}\int_x^{\infty}t^{a-1}e^{-t}dt$
  4. Error function ($erf$) and its inverse ($erf^{-1}$), where $erf = \frac{2}{\sqrt{\pi}}\int_0^xe^{-t^2}dt$
  5. $gcd$: Greatest Common Divisor of two numbers - key in the first number, followed by this button, then the second number, followed by the equals button. 
  6. $lcm$: Least Common Multiple of two numbers - operate in a manner similar to $gcd$
iOS App SciStatCalc screenshot Fourth segment - stats related function, Gamma function, upper and lower incomplete gamma function, error function, inverse error function, least common multiple, greatest common divisor, pi

The final segment ("Stack") contains Stack operations, where you can push a number on top of the stack, pop a number from the top of the stack, or clear the entire stack, as well as calculate the Sum, Average and Standard Deviation of all the numbers in the stack. The stack status is displayed in blue, directly below the main display. In addition, there are the reciprocal and factorial functions in this segment.

iOS App SciStatCalc screenshot Stack function - push, pop and clear a stack of numbers. reciprocal function, factorial function

In landscape mode, there are 17 distributions to choose from (using the left/right swipe gesture), listed alphabetically. For illustration purposes, the first distribution is shown. Two out of the three fields (Lower Limit, Upper Limit and Probability) must be filled in, as do all the relevant parameter fields - when the Calculate button is pressed, the sole blank field is updated.

For the screenshot below,
iOS App SciStatCalc screenshot Beta distribution - upper and lower limits, CDF, inverse CDF/ quantile evaluation

pressing Calculate results in

For the screenshot below,

pressing Calculate results in:-

For the screenshot below,

pressing Calculate results in:-

Also in landscape mode (when you swipe up), there are the following features:-
  1. Unpaired Student's t-test
  2. Paired Student's t-test
  3. Small sample hypothesis test
  4. Chi-squared test
  5. Tausworthe-based double precision Uniform Random Number Generator:-

iOS App SciStatCalc screenshot Statistical test - unpaired student's t-test, t-value, degrees of freedom, 95% confidence interval, null-hypothesis probability

iOS App SciStatCalc screenshot Paired student's t-test, t-value, degrees of freedom, standard error of difference

iOS App SciStatCalc screenshot Small sample hypothesis - t-value, mean value, probability threshold, 95% confidence interval, accept hypothesis

iOS App SciStatCalc screenshot chi-squared test, critical value, degrees of freedom

iOS App SciStatCalc screenshot Uniform Distribution Random Number Generator

Tuesday, 14 May 2013

Distributions processed by SciStatCalc

Below is a table in which are listed the 17 distributions whose CDF and inverse-CDF (also known as the quantile function) are computed by SciStatCalc. The table is embedded as a PDF file - feel free to download it. The table could come in handy as a quick reference guide for some attributes of the most popular distributions. The expression of the CDF occurs in the right most column.


Examining the table above, $I_x(a,b)$ denotes the normalised incomplete Beta function:-

The lower incomplete Gamma function $\gamma(a,x)$ is evaluated as:-
The Gamma function $\Gamma(a)$ is:-

The error function $erf(x)$ is:-