# What kind of distribution to model new business success

#### mthelm

##### New Member
BLS data show that the probability of a new business remaining in business after 1 year is 80%, after 2 years it's 70%, after 5 years it drops to 50% and the probability of still being around after 10 years is 30%. What kind of distribution can I use to model this? I've been searching online for a while and can't find the answer. I think for any specific year I could use a simple Bernoulli distribution; for example, for year two, I could use Bernoulli(0.7) to model the likelihood of a particular business surviving/failing at that point. However, I'd like to find a distribution that I can sample from that will allow me to determine the probability of survivng at time t. Any suggestions?

#### fed2

##### Active Member
looks like each time you double the time interval, you approximately square the survival probability? That suggests that you should be looking at the distribution of log of the failure times for modeling convenience. Its probably possible to derive an appropriate distribution from that information alone, but its not clickin' at the moment.

#### katxt

##### Active Member
The data looks somewhat like exponential decay, but if you want a distribution for say Monte Carlo risk analysis, you can always make a piece-wise function using the data you have.

#### fed2

##### Active Member
yeah i was going to say exponential, but its the log of the failure time thats exponential.

#### katxt

##### Active Member
Here is something you can experiment with. The graph shows the BLS data you mentioned in your first post - the first lot from 1994. The x axis is years from 1994 and the black line is 1/(1+0.2*years). kat

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#### mthelm

##### New Member
Here is something you can experiment with. The graph shows the BLS data you mentioned in your first post - the first lot from 1994. The x axis is years from 1994 and the black line is 1/(1+0.2*years). kat
Nice! This is perfect!