Calculating demand distribution of multi-step process
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It's been years since I've had to work with probabilities and I need to model a business problem, my situation is this: users are signing up for a service and I need to estimate future service requirements. I have an aggregate estimate of service signups over a period but but now I need to estimate both the likelihood of a particular prospect becoming a customer, as well as their future service needs.
Example
Step 1: 100 Prospects
Step 2: 30% will sign up over a 30 day period (a distribution)
Step 3: Survey Customer location and develop proposal (capacity: 2/day starting from sign-up)
Step 4: Customer signs off on proposal (a distribution, assume 1-10 days)
Step 5: Construction (capacity: 2/day, starting from sign-off)
Step 6: Set up service (capacity: 3/day, starting from construction completion)
The goal is to generate a demand-distribution for each step of the process.
In this example, a lot of this is driven by Step 2 and 4. Given the probability distribution of these steps, it drives demand for steps 3, 5 and 6, though daily capacity also figures. Also worth noting, I need to project demand by zipcode so (I think) I need to figure demand for each prospect, not just aggregate.
Finally, we'll start with an estimate but it needs to adjust for reality, So for example, on day 0 all 100 might have 1% chance of signing up, however on day 1, 10 sign up (say we get lucky), on day 2, those 10 now have 0% (because they've signed). While the remaining 90 still have 1%. Given this scenario, we might expect that greater than 30% will sign up in the 30-day period and adjust our probabilities upward.
probability probability-distributions
asked Jul 28 '13 at 22:53
stephanostephano
112
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add a comment |
$begingroup$
It's been years since I've had to work with probabilities and I need to model a business problem, my situation is this: users are signing up for a service and I need to estimate future service requirements. I have an aggregate estimate of service signups over a period but but now I need to estimate both the likelihood of a particular prospect becoming a customer, as well as their future service needs.
Example
Step 1: 100 Prospects
Step 2: 30% will sign up over a 30 day period (a distribution)
Step 3: Survey Customer location and develop proposal (capacity: 2/day starting from sign-up)
Step 4: Customer signs off on proposal (a distribution, assume 1-10 days)
Step 5: Construction (capacity: 2/day, starting from sign-off)
Step 6: Set up service (capacity: 3/day, starting from construction completion)
The goal is to generate a demand-distribution for each step of the process.
In this example, a lot of this is driven by Step 2 and 4. Given the probability distribution of these steps, it drives demand for steps 3, 5 and 6, though daily capacity also figures. Also worth noting, I need to project demand by zipcode so (I think) I need to figure demand for each prospect, not just aggregate.
Finally, we'll start with an estimate but it needs to adjust for reality, So for example, on day 0 all 100 might have 1% chance of signing up, however on day 1, 10 sign up (say we get lucky), on day 2, those 10 now have 0% (because they've signed). While the remaining 90 still have 1%. Given this scenario, we might expect that greater than 30% will sign up in the 30-day period and adjust our probabilities upward.
probability probability-distributions
asked Jul 28 '13 at 22:53
stephanostephano
112
$endgroup$
add a comment |
$begingroup$
It's been years since I've had to work with probabilities and I need to model a business problem, my situation is this: users are signing up for a service and I need to estimate future service requirements. I have an aggregate estimate of service signups over a period but but now I need to estimate both the likelihood of a particular prospect becoming a customer, as well as their future service needs.
Example
Step 1: 100 Prospects
Step 2: 30% will sign up over a 30 day period (a distribution)
Step 3: Survey Customer location and develop proposal (capacity: 2/day starting from sign-up)
Step 4: Customer signs off on proposal (a distribution, assume 1-10 days)
Step 5: Construction (capacity: 2/day, starting from sign-off)
Step 6: Set up service (capacity: 3/day, starting from construction completion)
The goal is to generate a demand-distribution for each step of the process.
In this example, a lot of this is driven by Step 2 and 4. Given the probability distribution of these steps, it drives demand for steps 3, 5 and 6, though daily capacity also figures. Also worth noting, I need to project demand by zipcode so (I think) I need to figure demand for each prospect, not just aggregate.
Finally, we'll start with an estimate but it needs to adjust for reality, So for example, on day 0 all 100 might have 1% chance of signing up, however on day 1, 10 sign up (say we get lucky), on day 2, those 10 now have 0% (because they've signed). While the remaining 90 still have 1%. Given this scenario, we might expect that greater than 30% will sign up in the 30-day period and adjust our probabilities upward.
probability probability-distributions
asked Jul 28 '13 at 22:53
stephanostephano
112
$endgroup$
It's been years since I've had to work with probabilities and I need to model a business problem, my situation is this: users are signing up for a service and I need to estimate future service requirements. I have an aggregate estimate of service signups over a period but but now I need to estimate both the likelihood of a particular prospect becoming a customer, as well as their future service needs.
Example
Step 1: 100 Prospects
Step 2: 30% will sign up over a 30 day period (a distribution)
Step 3: Survey Customer location and develop proposal (capacity: 2/day starting from sign-up)
Step 4: Customer signs off on proposal (a distribution, assume 1-10 days)
Step 5: Construction (capacity: 2/day, starting from sign-off)
Step 6: Set up service (capacity: 3/day, starting from construction completion)
The goal is to generate a demand-distribution for each step of the process.
In this example, a lot of this is driven by Step 2 and 4. Given the probability distribution of these steps, it drives demand for steps 3, 5 and 6, though daily capacity also figures. Also worth noting, I need to project demand by zipcode so (I think) I need to figure demand for each prospect, not just aggregate.
Finally, we'll start with an estimate but it needs to adjust for reality, So for example, on day 0 all 100 might have 1% chance of signing up, however on day 1, 10 sign up (say we get lucky), on day 2, those 10 now have 0% (because they've signed). While the remaining 90 still have 1%. Given this scenario, we might expect that greater than 30% will sign up in the 30-day period and adjust our probabilities upward.
probability probability-distributions
probability probability-distributions
asked Jul 28 '13 at 22:53
stephanostephano
112
asked Jul 28 '13 at 22:53
stephanostephano
112
edited Jul 29 '13 at 1:32
stephano
asked Jul 28 '13 at 22:53
stephanostephano
112
asked Jul 28 '13 at 22:53
stephanostephano
112
asked Jul 28 '13 at 22:53
stephanostephano
112
112
add a comment |
add a comment |
1 Answer
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There are two interpretations of this. The first is if you just care about the number of users signed up on given days. This is essentially a multinomial distribution. We have $d=30$ days. Each user goes into a particular day and we have something like $n=30$ users. The chance that a user goes into a day is independent of anyone else and is equal throughout all days, and is equal to $p=1/d$. Let $N=(n_1,n_2,ldots,n_d)$ be the vector of users where $n_i$ is the number of users signed up on day $i$. Clearly $sum_{i=1}^dn_i=n$. Then
$$P(N=(n_1,ldots,n_d))=frac{n!}{n_1!cdots n_d!}p^n$$
Otherwise, if you label the users $1,2,..,n$, the chance of the users signing up on individually prescribed dates (say user 1 on day 4, user 2 on day 20, etc), is always $p^n$.
answered Jul 28 '13 at 23:41
Alex R.Alex R.
25k12452
$endgroup$
$begingroup$
Thank you! <br/><br/>I need to develop probabilities for each customer (each customer has a zipcode and we need to project demand by zipcode). We start with a projection but then the model needs to account for actual signups. For example, on day 0 all 100 might 1% chance of signing up, however on day 1, 10 sign up (we get lucky), now on day 2 those 10 have 0% (they've signed). The remaining 90still have 1%, etc.<br/><br/> This process has about 10 steps with variable amounts of lag for each step, so the eventual goal is to generate a demand-distribution for each step of the process.
$endgroup$
– stephano
Jul 29 '13 at 0:05
$begingroup$
Note: I substantially updated the problem description to clarify problem after this answer was submitted (many thanks!)
$endgroup$
– stephano
Jul 29 '13 at 1:35
add a comment |
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1 Answer
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1 Answer
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$begingroup$
There are two interpretations of this. The first is if you just care about the number of users signed up on given days. This is essentially a multinomial distribution. We have $d=30$ days. Each user goes into a particular day and we have something like $n=30$ users. The chance that a user goes into a day is independent of anyone else and is equal throughout all days, and is equal to $p=1/d$. Let $N=(n_1,n_2,ldots,n_d)$ be the vector of users where $n_i$ is the number of users signed up on day $i$. Clearly $sum_{i=1}^dn_i=n$. Then
$$P(N=(n_1,ldots,n_d))=frac{n!}{n_1!cdots n_d!}p^n$$
Otherwise, if you label the users $1,2,..,n$, the chance of the users signing up on individually prescribed dates (say user 1 on day 4, user 2 on day 20, etc), is always $p^n$.
answered Jul 28 '13 at 23:41
Alex R.Alex R.
25k12452
$endgroup$
$begingroup$
Thank you! <br/><br/>I need to develop probabilities for each customer (each customer has a zipcode and we need to project demand by zipcode). We start with a projection but then the model needs to account for actual signups. For example, on day 0 all 100 might 1% chance of signing up, however on day 1, 10 sign up (we get lucky), now on day 2 those 10 have 0% (they've signed). The remaining 90still have 1%, etc.<br/><br/> This process has about 10 steps with variable amounts of lag for each step, so the eventual goal is to generate a demand-distribution for each step of the process.
$endgroup$
– stephano
Jul 29 '13 at 0:05
$begingroup$
Note: I substantially updated the problem description to clarify problem after this answer was submitted (many thanks!)
$endgroup$
– stephano
Jul 29 '13 at 1:35
add a comment |
$begingroup$
There are two interpretations of this. The first is if you just care about the number of users signed up on given days. This is essentially a multinomial distribution. We have $d=30$ days. Each user goes into a particular day and we have something like $n=30$ users. The chance that a user goes into a day is independent of anyone else and is equal throughout all days, and is equal to $p=1/d$. Let $N=(n_1,n_2,ldots,n_d)$ be the vector of users where $n_i$ is the number of users signed up on day $i$. Clearly $sum_{i=1}^dn_i=n$. Then
$$P(N=(n_1,ldots,n_d))=frac{n!}{n_1!cdots n_d!}p^n$$
Otherwise, if you label the users $1,2,..,n$, the chance of the users signing up on individually prescribed dates (say user 1 on day 4, user 2 on day 20, etc), is always $p^n$.
answered Jul 28 '13 at 23:41
Alex R.Alex R.
25k12452
$endgroup$
$begingroup$
Thank you! <br/><br/>I need to develop probabilities for each customer (each customer has a zipcode and we need to project demand by zipcode). We start with a projection but then the model needs to account for actual signups. For example, on day 0 all 100 might 1% chance of signing up, however on day 1, 10 sign up (we get lucky), now on day 2 those 10 have 0% (they've signed). The remaining 90still have 1%, etc.<br/><br/> This process has about 10 steps with variable amounts of lag for each step, so the eventual goal is to generate a demand-distribution for each step of the process.
$endgroup$
– stephano
Jul 29 '13 at 0:05
$begingroup$
Note: I substantially updated the problem description to clarify problem after this answer was submitted (many thanks!)
$endgroup$
– stephano
Jul 29 '13 at 1:35
add a comment |
$begingroup$
There are two interpretations of this. The first is if you just care about the number of users signed up on given days. This is essentially a multinomial distribution. We have $d=30$ days. Each user goes into a particular day and we have something like $n=30$ users. The chance that a user goes into a day is independent of anyone else and is equal throughout all days, and is equal to $p=1/d$. Let $N=(n_1,n_2,ldots,n_d)$ be the vector of users where $n_i$ is the number of users signed up on day $i$. Clearly $sum_{i=1}^dn_i=n$. Then
$$P(N=(n_1,ldots,n_d))=frac{n!}{n_1!cdots n_d!}p^n$$
Otherwise, if you label the users $1,2,..,n$, the chance of the users signing up on individually prescribed dates (say user 1 on day 4, user 2 on day 20, etc), is always $p^n$.
answered Jul 28 '13 at 23:41
Alex R.Alex R.
25k12452
$endgroup$
There are two interpretations of this. The first is if you just care about the number of users signed up on given days. This is essentially a multinomial distribution. We have $d=30$ days. Each user goes into a particular day and we have something like $n=30$ users. The chance that a user goes into a day is independent of anyone else and is equal throughout all days, and is equal to $p=1/d$. Let $N=(n_1,n_2,ldots,n_d)$ be the vector of users where $n_i$ is the number of users signed up on day $i$. Clearly $sum_{i=1}^dn_i=n$. Then
$$P(N=(n_1,ldots,n_d))=frac{n!}{n_1!cdots n_d!}p^n$$
Otherwise, if you label the users $1,2,..,n$, the chance of the users signing up on individually prescribed dates (say user 1 on day 4, user 2 on day 20, etc), is always $p^n$.
answered Jul 28 '13 at 23:41
Alex R.Alex R.
25k12452
edited Jul 28 '13 at 23:54
answered Jul 28 '13 at 23:41
Alex R.Alex R.
25k12452
answered Jul 28 '13 at 23:41
Alex R.Alex R.
25k12452
answered Jul 28 '13 at 23:41
Alex R.Alex R.
25k12452
25k12452
$begingroup$
Thank you! <br/><br/>I need to develop probabilities for each customer (each customer has a zipcode and we need to project demand by zipcode). We start with a projection but then the model needs to account for actual signups. For example, on day 0 all 100 might 1% chance of signing up, however on day 1, 10 sign up (we get lucky), now on day 2 those 10 have 0% (they've signed). The remaining 90still have 1%, etc.<br/><br/> This process has about 10 steps with variable amounts of lag for each step, so the eventual goal is to generate a demand-distribution for each step of the process.
$endgroup$
– stephano
Jul 29 '13 at 0:05
$begingroup$
Note: I substantially updated the problem description to clarify problem after this answer was submitted (many thanks!)
$endgroup$
– stephano
Jul 29 '13 at 1:35
add a comment |
$begingroup$
Thank you! <br/><br/>I need to develop probabilities for each customer (each customer has a zipcode and we need to project demand by zipcode). We start with a projection but then the model needs to account for actual signups. For example, on day 0 all 100 might 1% chance of signing up, however on day 1, 10 sign up (we get lucky), now on day 2 those 10 have 0% (they've signed). The remaining 90still have 1%, etc.<br/><br/> This process has about 10 steps with variable amounts of lag for each step, so the eventual goal is to generate a demand-distribution for each step of the process.
$endgroup$
– stephano
Jul 29 '13 at 0:05
$begingroup$
Note: I substantially updated the problem description to clarify problem after this answer was submitted (many thanks!)
$endgroup$
– stephano
Jul 29 '13 at 1:35
$begingroup$
Thank you! <br/><br/>I need to develop probabilities for each customer (each customer has a zipcode and we need to project demand by zipcode). We start with a projection but then the model needs to account for actual signups. For example, on day 0 all 100 might 1% chance of signing up, however on day 1, 10 sign up (we get lucky), now on day 2 those 10 have 0% (they've signed). The remaining 90still have 1%, etc.<br/><br/> This process has about 10 steps with variable amounts of lag for each step, so the eventual goal is to generate a demand-distribution for each step of the process.
$endgroup$
– stephano
Jul 29 '13 at 0:05
$begingroup$
Thank you! <br/><br/>I need to develop probabilities for each customer (each customer has a zipcode and we need to project demand by zipcode). We start with a projection but then the model needs to account for actual signups. For example, on day 0 all 100 might 1% chance of signing up, however on day 1, 10 sign up (we get lucky), now on day 2 those 10 have 0% (they've signed). The remaining 90still have 1%, etc.<br/><br/> This process has about 10 steps with variable amounts of lag for each step, so the eventual goal is to generate a demand-distribution for each step of the process.
$endgroup$
– stephano
Jul 29 '13 at 0:05
$begingroup$
Note: I substantially updated the problem description to clarify problem after this answer was submitted (many thanks!)
$endgroup$
– stephano
Jul 29 '13 at 1:35
$begingroup$
Note: I substantially updated the problem description to clarify problem after this answer was submitted (many thanks!)
$endgroup$
– stephano
Jul 29 '13 at 1:35
add a comment |
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