Questions tagged [logarithmic-series]

Use this tag to refer to the (discrete) logarithmic-series distribution.

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How do I show $$ \int_{0}^{1} exp(-f(x))dx=\sum_{n=0}^{\infty} \frac{(-1)^n}{n!} \int_{0}^{\infty} f(x)^n dx $$ [migrated]

I have been given a function f(x) defined on the interval $$[0;\infty[ $$ by the formula $$ \begin{array}{cc} \ f(x)= \{ & \begin{array}{cc}\ 0 & x= 0 \\ \ x\space log(x) ...
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44 views

How to depict a histogram with a wide range of negative/positive data? Is this logarithmic?

I want to show some data on a range from -50 to 20 and I especially want to show the details as values approach 0. The graph of the data is shown below. The problem is what do you call such a scale. ...
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Multivariate Natural Logarithmic (Exponential) Regression

I have a list of values with 4 input columns and one output column as follows: Temperature: Directly Proportional to Severity Hours of utilization per month: Directly Proportional to Severity Power ...
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61 views

Order statistics for log series distribution?

I am trying to obtain the probability mass function for various order statistics of a log series distribution for a given $n$. To do so, I tried modifying the code given in this question: Simulating ...
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131 views

Which type of regression model for count data should I use for log-series?

I am attempting to identify the effects of mealtime habits on fast food consumption. In this case, the dependent variable is number of times per week a respondent reported eating fast food. As this is ...
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55 views

Using probability for estimate event time

I have dataset about file creation durring a year. From this dataset I extract subset for days when user created just one file. there is information (timestamp) when that happened. I created a bins ...
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47 views

How to calculate the mean of a certain urn experiment

I'm sorry if my style of formulation is a bit sloppy Let us assume that we have an abstract urn with balls having $S$ different colors. The probbility that the color $i$ ranging from $1..S$ has $n$ ...
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129 views

How to interpret a dataset with a pseudo-logarithmic trend?

I am dealing with a scatterplot where I am trying to figure out the relationship between two variables, but I have so far failed to identify what the best fit could be. The presence of ...
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104 views

HOMEWORK: Proving Log-Series Distribution

This is just a quick query to confirm that I have this right and that my way of constructing it is correct. We were asked to prove: $a=\frac{-1}{log(1-\theta)}$ for $p(x)=a\frac{\theta^x}{x}$ for $...
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Closed form function relating $\mu$ to the natural parameter for the logarithmic series distribution?

While answering another question here, I mentioned the logarithmic series distribution as a possible model for species per genus. In the course of looking at the pmf while answering that I realized ...