Skip to main content

graphics - How can I extract the maximum value from a Histogram?


In Mathematica 8.04 I've created a histogram of returns on a stock using:


returns = FinancialData["SP500", "Return", {Date[] - {5, 0, 0, 0, 0, 0}, Date[]}, "Value"];
μ = Mean[returns];
h = Histogram[returns, 300, "PDF"];

Mathematica graphics



where "returns" is a list of the daily returns, and I want 300 bins in the probability density method. Next, I would like to draw a line that represents the mean of the returns so I use:


meanLine = Graphics[{Thick, Darker[Green], Line[{{μ, 0}, {μ, maxFreq + 2}}]}];

The problem is that I need to calculate the highest y-value for the line, which should be equal to the count of the data points in the bin with the most points (I've called this maxFreq above). I am currently setting this value manually because I don't know how to extract it from the histogram (h). Note that the x-coordinate of this line (μ) is simply the mean of the returns.


I've tried looking at FullForm[h] to see if I could figure out how to extract the data. Buried within that output is the following:


List[List[Rectangle[List[-0.0015, 0.], List[-0.001, 54.0111]

which shows that I want to set maxFreq = 54.0111. So, I suppose that I want to use the Max function, but I don't know how to access the heights of each bin. I think that I need to use some variation of the Part function, but I can't figure out how. Any clues would be appreciated.


Here is the code that will generate what I'm looking for, but maxFreq is manually entered:


returns = FinancialData["SP500", "Return", {Date[] - {5, 0, 0, 0, 0, 0}, Date[]}, "Value"];

μ = Mean[returns];
h = Histogram[returns, 300, "PDF"];
maxFreq = 54;
meanLine = Graphics[{Thick, Darker[Green],Line[{{μ, 0}, {μ, maxFreq + 2}}]}];
Show[h, meanLine]

Answer



As mentioned by others, use HistogramList. You can even use the resulting information to generate the plot without recomputing the information:


{bins, heights} = HistogramList[returns, 300, "PDF"];
maxFreq = Max[heights];
Histogram[returns, {bins}, heights &,

Epilog -> {{Thick, Darker[Green],
Line[{{μ, 0}, {μ, maxFreq + 2}}]}}]

enter image description here


Comments

Popular posts from this blog

plotting - How to draw lines between specified dots on ListPlot?

I would like to create a plot where I have unconnected dots and some connected. So far, I have figured out how to draw the dots. My code is the following: ListPlot[{{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4,13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full] I have thought using ListLinePlot command, but I don't know how to specify to the command to draw only selected lines between the dots. Do have any suggestions/hints on how to do that? Thank you. Answer One possibility would be to use Epilog with Line : ListPlot[ {{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4, 13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full, Epilog -> { Line[ ...

dynamic - How can I make a clickable ArrayPlot that returns input?

I would like to create a dynamic ArrayPlot so that the rectangles, when clicked, provide the input. Can I use ArrayPlot for this? Or is there something else I should have to use? Answer ArrayPlot is much more than just a simple array like Grid : it represents a ranged 2D dataset, and its visualization can be finetuned by options like DataReversed and DataRange . These features make it quite complicated to reproduce the same layout and order with Grid . Here I offer AnnotatedArrayPlot which comes in handy when your dataset is more than just a flat 2D array. The dynamic interface allows highlighting individual cells and possibly interacting with them. AnnotatedArrayPlot works the same way as ArrayPlot and accepts the same options plus Enabled , HighlightCoordinates , HighlightStyle and HighlightElementFunction . data = {{Missing["HasSomeMoreData"], GrayLevel[ 1], {RGBColor[0, 1, 1], RGBColor[0, 0, 1], GrayLevel[1]}, RGBColor[0, 1, 0]}, {GrayLevel[0], GrayLevel...

Is there a way to do conditional matrix loop using 'continue'

I have the following: n = 3; m = 5; ww = RandomReal[{0, 0.1}, {n, n}]; uu = RandomReal[{0, 1}, {m, n}]; pp = RandomReal[{0, 1}, {n, n}]; ss = RandomInteger[{0, 5}, {m, n}]; Grid[{{"ww", "uu", "pp", "ss"}, {ww // TableForm, uu // TableForm, pp // TableForm, ss // TableForm}}, Spacings -> {5, 2}, Dividers -> All] where I would like to look at every element of matrix ss and produce a matrix tt , with zeroes at the locations in ss which have zeroes, and in all other positions do the following: tt = (-1/Subscript[ww, m]) Log[(1 - uu)/(Subscript[pp, m - 1])], where Subscript[ww, m] is the value at index of ww matrix and where Subscript[pp, m - 1] is the value at index-1 of pp matrix. So for example if the first value ever read from matrix ss happens to be 2, then value taken from matrix ww would be from the row 2, but from pp would be from row 1. Also how to tell difference between a 0 as a valid value from within the matrix elemen...