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Histogram
1. Suppose X is a random variable with the pdf 
where b > 0. Suppose we can generate observations from f(z). Explain how we can generate observations from 
.
2. Determine a method to generate random observations for the logistic pdf, (4.4.11). Write an R function that returns a random sample of observations from a logistic distribution. Use your function to generate 10,000 observations from this pdf. Then obtain a histogram (use hist(x,pr=T), where x contains the observations). On this histogram overlay a plot of the pdf.
Histogram
The statistician Karl Pearson coined the term “histogram” as a reference to a certain “graphical representation” (Ioannidis, 2003). The graphic representation was characterized by columns marks of frequency parallel to the range of their base. Today, the histogram tool provides a histogram which is the cumulative distribution of a single dataset by displaying the frequencies of data falling in a set of continuous value ranges. The tool also provides a smooth plot of the empirical density. When the density plot has not been selected, frequencies are displayed but when selected it displays probabilities.
Steps to use the tool on Excel
- On Excel, one opens the File, then moves to Options.
- On the Excel Options dialog box, click Add-Ins then click Excel Add-Ins then click Go.
- This leads to various analysis tools, select Analysis ToolPak then OK.
- Once the tool opens, one prepares by selecting the bin range in ascending order. The Excel histogram should have a limited input data range. This procedure is meant to enable the Analysis ToolPak.
- One creates the histogram, by moving to DATA > Data Analysis> Histogram.
- On the Histogram dialog, one specifies the input range and the Bin rage.
- One then selects the Output options. The output table and histogram are pasted in a new sheet.
- Finally, the data is presented.
The Excel Histogram tool is readily available and easy to use.
Advantage and Disadvantage
The Histogram tool makes it easier to recognize different frequencies of data occurring in datasets (Benham, 2017). However, the tool can present outcomes that are misleading especially where too many datasets are involved since analysis becomes problematic while too few can leave out essential data (Benham, 2017). It can only analyze two sets of data.
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References
Benham, S. (2017, June 15). Purpose of a Histogram. Sciencing. https://sciencing.com/purpose-histogram-10024024.html
Ioannidis, Y. (2003). The History of Histograms (abridged). Proceedings 2003 VLDB Conference, 19-30. https://doi.org/10.1016/b978-012722442-8/50011-2