Histogram
A Histogram tabulates data into bins. The user must specify the break points of the bins, b0, b1, b2, ..., bk, where there are k+1 break points, and k bins. b0 may be Double.NEGATIVE_INFINITY and bk may be Double.POSITIVE_INFINITY.
If only one break point is supplied, then the bins are automatically defined as: (Double.NEGATIVE_INFINITY, b0] and (b0, Double.POSITIVE_INFINITY).
If two break points are provided, then there is one bin: [b0, b1), any values less than b0 will be counted as underflow and any values [b1, +infinity) will be counted as overflow.
If k+1 break points are provided then the bins are defined as: [b0,b1), [b1,b2), [b2,b3), ..., [bk-1,bk) and any values in (-infinity, b0) will be counted as underflow and any values [bk, +infinity) will be counted as overflow. If b0 equals Double.NEGATIVE_INFINITY then there can be no underflow. Similarly, if bk equals Double.POSITIVE_INFINITY there can be no overflow.
The break points do not have to define equally sized bins. Static methods within companion object are provided to create equal width bins and to create histograms with common characteristics.
If any presented value is Double.NaN, then the value is counted as missing and the observation is not tallied towards the total number of observations. Underflow and overflow counts also do not count towards the total number of observations.
Statistics are also automatically collected on the collected observations. The statistics do not include missing, underflow, and overflow observations. Statistics are only computed on those observations that were placed (counted) within some bin.
Parameters
the break points for the histogram and must be strictly increasing
an optional name for the histogram
Properties
Returns an array of Bins based on the current state of the histogram
Returns a List of Bins based on the current state of the histogram
Gets the sum of squares of the deviations from the average This is the numerator in the classic sample variance formula
Lower limit of first histogram bin.
Gets the lag-1 generate correlation of the unweighted observations. Note: See Box, Jenkins, Reinsel, Time Series Analysis, 3rd edition, Prentice-Hall, pg 31
Gets the lag-1 generate covariance of the unweighted observations. Note: See Box, Jenkins, Reinsel, Time Series Analysis, 3rd edition, Prentice-Hall, pg 31
Upper limit of the last histogram bin.
Counts the number of observations that were negative, strictly less than zero.
Counts of values located above the last bin.
Gets the standard error of the observations. Simply the generate standard deviation divided by the square root of the number of observations
Total number of observations collected including overflow and underflow
Counts of values located below the first bin.
Gets the Von Neumann Lag 1 test statistic for checking the hypothesis that the data are uncorrelated Note: See Handbook of Simulation, Jerry Banks editor, McGraw-Hill, pg 253.
Functions
The bin that x falls in. The bin is a copy. It will not reflect observations collected after this call.
Returns an instance of a Bin for the supplied bin number The bin does not reflect changes to the histogram after this call. May throw IndexOutOfBoundsException
Returns the fraction of the data relative to those tabulated in the bins for the bin number associated with the x
Returns the fraction of the data relative to those tabulated in the bins for the supplied bin number
Return a copy of the information as an instance of a statistic
Returns the cumulative count of all bins up to and including the bin containing the value x
Returns the cumulative count of all the bins up to and including the indicated bin number
Returns the cumulative fraction of the data up to and including the bin containing the value of x
Returns the cumulative fraction of the data up to and including the indicated bin number
Returns the cumulative count of all the data (including underflow and overflow) for all bins up to and including the bin containing x
Returns the cumulative count of all the data (including underflow and overflow) up to and including the indicated bin
Returns the cumulative fraction of all the data up to an including the bin containing the value x, (includes over and under flow)
Returns the cumulative fraction of all the data up to and including the supplied bin (includes over and under flow)
Computes the right most meaningful digit according to (int)Math.floor(Math.log10(a*getStandardError())) See doi 10.1287.opre.1080.0529 by Song and Schmeiser