# Getting PDF from imported Histogram

So I'd like to create a probability density function from an existing histogram from a program that I use. My input data is of the form

bin    hits
0.     0
0.025  0
0.05   0
0.075 15
0.1   97

etc.


and I imported it into Mathematica the following way

data

{{0.,0},{0.025,0},{0.05,0},{0.075,15},{0.1,97},...}


I want to read this data and create a probability density from it. The end goal is to then RandomVariate around this pdf:

pdf = HistogramDistribution[data, {bins[[1]], bins[[-1]], bwidth}]
new_data = RandomVariate[pdf,n]


My first attempt was to use HistogramDistribution to create a PDF from the imported Histogram - since this requires a set of data points, I attempted the following:

For[j = 1, j < Length[data] + 1, j++,
For[k = 0, k < data[[j]][[2]], k++,
AppendTo[temphisto, data[[j]][[1]]]
]
];

pdf = HistogramDistribution[temphisto, {bins[[1]], bins[[-1]], bwidth}];


Of course, this gets unnecessarily time consuming once I crank up the initial histogram entries and it also feels redundant to do so since I can achieve the output of HistogramList right from the start:

HistogramList[temphisto, {bins[[1]], bins[[-1]], bwidth}]

{{0.,0.025,0.05,0.075,0.1,...},
{0,0,0,15,97,...}}


Is there a way to turn the output from HistogramList to a HistogramDistribution or maybe create a probability density function from an imported histogram?

Thanks for the aid!

Try WeightedData using the second column as weights vector:

SeedRandom[1]
data = Transpose[{Range[0, 1, .05], RandomInteger[50, 21]}];
data // TableForm // TeXForm


$\begin{array}{cc} 0. & 20 \\ 0.05 & 1 \\ 0.1 & 48 \\ 0.15 & 2 \\ 0.2 & 6 \\ 0.25 & 3 \\ 0.3 & 16 \\ 0.35 & 28 \\ 0.4 & 33 \\ 0.45 & 31 \\ 0.5 & 33 \\ 0.55 & 17 \\ 0.6 & 12 \\ 0.65 & 44 \\ 0.7 & 40 \\ 0.75 & 30 \\ 0.8 & 24 \\ 0.85 & 2 \\ 0.9 & 25 \\ 0.95 & 11 \\ 1. & 21 \\ \end{array}$

{bins, counts} = Transpose[data];
wd = WeightedData[bins, counts];
dist = HistogramDistribution[wd]


SeedRandom[1]