startweb.esttest function

Opens default web browser and loads a web page for length estimation and testing.

Function startweb.esttest() opens a web browser and loads the page for length estimation and hypothesis testing of data read from a picture. Use this function if you would like to compute the length of an interval, which is the domain of uniform distribution, but the data are contaminated with additive error. Sequence of actions on the web page is as follows:

1. Load a picture in JPG format
2. Click on start and end point of the line passing through the observed object
3. Set data preparation parameters
4. Click on generate data so the data are prepared
5. • set estimation parameters (see lengthest) and click on Estimate, or
   • set testing parameters (see lengthtest) and click on Test.

startweb.esttest()

Details

Parameters that can be set on the web page are as follows:

Data parameters

• Levels of grey: Number of colors (shades of grey) used in analysis.
• Box size: The algorithm takes each pixel of a picture and maps it to box_size * box_size matrix. It is done in a way that the brightness of the observed pixel dictates the quantity of dots in mentioned matrix. Distribution of dots in matrix is uniform. Ultimately, length estimation or testing is done on the set of the resulting matrices.
• Line thickness: Width of the line, i.e. the maximum length between surrounding pixel and the drawn line so that pixel is to be taken into account for length estimation or hypothesis testing. All surrounding pixels are orthogonally projected on the line.
• Observed object is...: Sets whether observed object is bright or dark.

Estimation parameters

• Error distribution: The type of the error distribution. Can be Gauss, Laplace, T1, T2, T3, T4 or T5 (Student).
• Error standard deviation: Estimation method for the error standard deviation. Can be Maximum Likelihood (ML) or the Method of Moments. If one does not want to estimate the deviation but to explicitly enter it, he should choose "Enter value" and enter the deviation in the lower field.
• Confidence level: Confidence level of the confidence interval.

Testing parameters

• $H_0$: Specified null value being tested (measured in pixel width or percentage of image width).
• Alternative: The alternative hypothesis. Can be less, greater or two-sided.

Results

• Length expressed in pixel width, as well as in percentage of the whole image's width
• Standard deviation
• Method - Asymptotic distribution of MLE or LR statistic
• Confidence interval
• p-value of the test and the value of the test statistic (if hypothesis testing has been performed)

Note

In order to have quadratic pixels on the screen, please use proportional screen resolution. In the case of modern LCD (LED) displays, these are usually native screen resolutions. If your display has aspect ratio width:height = 16:9, these resolutions are 1280x720, 1600x900, 1920x1080, etc. In the case od 16:10 display, use 1280x800, 1440x900, 1920x1200, etc. If you use nonproportional screen resolution, pixels on the screen will not be quadratic, so estimated values measured in pixels may not be correct.

Examples

# open the web page for length estimation and hypothesis testing of an
# object shown in the picture
startweb.esttest()