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 Short-Term Actuarial Math Old Exam C Forum

#1
11-10-2017, 01:49 PM
 Bash Member SOA Join Date: Jun 2010 Posts: 60
MLEs

I need some explanations to mle truncation and censoring.

1.
a) What does it mean to say a data value is left censored at d?
b) How will an exam question be worded for left censored?
c) If a question says "values below 50 were not reported, would that be left truncated or left censored?

2.
a) What does it mean to say a data value is right truncated at u?
b) How will an exam question be worded for right truncated?
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#2
11-10-2017, 06:55 PM
 Seasplash Member CAS SOA Join Date: Jun 2014 Location: Arlington, VA Studying for MLC College: Cal Poly San Luis Obispo Posts: 301

Quote:
 Originally Posted by Bash I need some explanations to mle truncation and censoring. 1. a) What does it mean to say a data value is left censored at d? b) How will an exam question be worded for left censored? c) If a question says "values below 50 were not reported, would that be left truncated or left censored? 2. a) What does it mean to say a data value is right truncated at u? b) How will an exam question be worded for right truncated?
1)
a) A data value that is left-censored at d is a value that you know is below d, but don't know the exact value. Left-censoring is rare.
b) I think it'll be pretty straight-forward. A pretty silly example is as follows: There is a awkward scale that will display your weight if you weigh more than 100 pounds. A skinny person weighs himself on this scale but his weight is not shown. This person's weight is left-censored at 100.
c) If it says "values below 50 were not reported", then that means those values are truncated because you know absolutely nothing. If values were left-censored at d then you would know how many values are censored (e.g 5 values are less than 50).

2)
a) A value that is right-truncated at u means you know absolutely nothing from u and above.
b) I think it'll be pretty straight-forward. An example of right-truncation is: "XYZ factory receives light-bulbs that are less than 6 ounces. Light-bulbs heavier than 6 ounces are shipped to a different factory."
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#3
11-11-2017, 12:38 PM
 Jim Daniel Member SOA Join Date: Jan 2002 Location: Davis, CA College: Wabash College B.A. 1962, Stanford Ph.D. 1965 Posts: 2,669

Quote:
 Originally Posted by Bash I need some explanations to mle truncation and censoring. 1. a) What does it mean to say a data value is left censored at d? b) How will an exam question be worded for left censored? c) If a question says "values below 50 were not reported, would that be left truncated or left censored? 2. a) What does it mean to say a data value is right truncated at u? b) How will an exam question be worded for right truncated?
Almost all C/4 problems with censoring or truncation have right censoring and left truncation. Note that if X is instead left censored and right truncated, then 1/X is right censored and left truncated, which could make it easier to use the distribution of 1/X.
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#4
11-14-2017, 06:54 PM
 Bash Member SOA Join Date: Jun 2010 Posts: 60
mle

Thanks to Seasplash and Jim. I would be looking at questions more as left truncated and right censored except the question specifically states left censored and right truncated, in which case I would consider the distribution of 1/x as left truncated and right censored. I believe this is a fair assumption.
__________________
P FM MFE C MLC
VEE: Statistics Corporate Finance Economics