Video Tutorial – Obtaining the Expected Value of the Exponential Distribution Using the Moment Generating Function

In this video tutorial on YouTube, I use the exponential distribution’s moment generating function (MGF) to obtain the expected value of this distribution.  Visit my YouTube channel to watch more video tutorials!


Forgot a new co-worker’s name? This could be an opportunity to establish a positive relationship.

Meeting new people is a constant part of my life, whether it is through new jobs, social events, or networking events.  The first task in establishing rapport with a new acquaintance is to learn their name, yet I sometimes forget it after our first conversation.

shake hands.jpeg

Image courtesy of on Pexels.

Forgetting new names is very common and forgivable, especially if you are meeting many new people at once.  However, I notice that most people are afraid to admit this.  Perhaps they are embarrassed or worried that their new acquaintances will feel offended.  Thus, they often greet them many times without referencing their name, and this could continue for days, weeks, or even months!

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Remove leading blanks when creating macro variables using PROC SQL in SAS

I regularly use PROC SQL to create macro variables in SAS, and I recently noticed a strange phenomenon when resolving a macro variable within double quotation marks in the title of a plot.  Thankfully, I was able to replicate this problem using the SASHELP.BASEBALL data set, which is publicly available.  I was then able to send the code and the strange result to SAS Technical Support for their examination.

proc sql;
     select count(name)
     into   :hitters_100plusHR
     where  CrHome > 100;

proc sgplot
     data =;
     histogram Salary;
     title1 'Distribution of salaries';
     title2 "Restricted to the &hitters_100plusHR hitters with more than 100 career home runs";


Here is the resulting plot.  Notice the extra spaces before “72” in the title of the plot.

SAS Technical Support informed me that

  • this problem is commonly known.
  • there is no way of predicting when it will occur
  • for now, the best way to deal with it is to remove the leading blanks using one of several ways.

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Use unique() instead of levels() to find the possible values of a factor in R

*In a previous version of this blog post, I incorrectly wrote that “Species” is a character variable.  Instead, it is a factor.  I thank the readers who corrected me in the comments.

When I first encountered R, I learned to use the levels() function to find the possible values of a categorical variable.  However, I recently noticed something very strange about this function.

Consider the built-in data set “iris” and its factor “Species”.  Here are the possible values of “Species”, as shown by the levels() function.

> levels(iris$Species)

[1] "setosa" "versicolor" "virginica"

Now, let’s remove all rows containing “setosa”.  I will use the table() function to confirm that no rows contain “setosa”, and then I will apply the levels() function to “Species” again.

> iris2 = subset(iris, Species != 'setosa')
> table(iris2$Species)

    setosa versicolor virginica 
         0         50        50 

> levels(iris2$Species)

[1] "setosa" "versicolor" "virginica"

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Video Tutorial – The Moment Generating Function of the Exponential Distribution

In this video tutorial on YouTube, I derive the moment generating function (MGF) of the exponential distribution.  Visit my YouTube channel to watch more video tutorials!

A SAS macro to automatically label variables using another data set


When I write SAS programs, I usually export the analytical results into an output that a client will read.  I often cannot show the original variable names in these outputs; there are 2 reasons for this:

  • The maximal length of a SAS variable’s name is 32 characters, whereas the description of the variable can be much longer.  This is the case for my current job in marketing analytics.
  • Only letters, numbers, and underscores are allowed in a SAS variable’s name.  Spaces and special characters are not allowed.  Thus, if a variable’s name is quite long and complicated to describe, then the original variable name would be not suitable for presentation or awkward to read.  It may be so abbreviated that it is devoid of practical meaning.

This is why labelling variables can be a good idea.  However, I usually label variables manually in a DATA step or within PROC SQL, which can be very slow and prone to errors.  I recently worked on a data set with 193 variables, most of which require long descriptions to understand what they mean.  Labelling them individually and manually was not a realistic method, so I sought an automated or programmatic way to do so.

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