# Functions block

**URL:** <https://discourse.mc-stan.org/t/functions-block/27832>\
**Category:** General\
**Created:** [June 15, 2022, 9:40am UTC](https://discourse.mc-stan.org/t/functions-block/27832 "2022-06-15T09:40:24Z")\
**Posts on this page:** 19\
**Page:** 1

<div class="post-metadata">

**Author:** ![Laxmi\_Pd\_Sapkota](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/laxmi_pd_sapkota/32/11814_2.png) [@Laxmi\_Pd\_Sapkota](https://discourse.mc-stan.org/u/Laxmi_Pd_Sapkota)\
**Post date:** [June 15, 2022, 9:40am UTC](https://discourse.mc-stan.org/t/functions-block/27832/1 "2022-06-15T09:40:24Z")

</div>

Dear all, I am just started to use Stan and I am confusing whether we have to enter log of PDF function or the sum of the log of the PDF function in the functions block using the `real _lpdf() `signature. I have found that some authors have entered `_lpdf `with sum function in the functions block.([Extreme value analysis and user defined probability functions in Stan](https://mc-stan.org/users/documentation/case-studies/gpareto_functions.html)). I have shared my stan code below please suggest to me whether my code is correct or not.

```nohighlight

functions{
  real OLGE_lpdf(real y, real a, real b, real delta, real theta){
    real z;
    real w;
    z = (1 - exp(-b*y))^a;
    w = (log(a)+log(b)+ theta*log(delta)+log(theta)- b*(y) + (a-1)*(log1m(exp(-b*y)))-
  2*log1m(z) - (theta+1)*log(delta + (z/(1-z)))); //this is my pdf just taking log
  return w;
}
  real OLGE_rng(real a, real b, real delta, real theta){
    real u;
    real v;
    u = uniform_rng(0, 1);
    v = (((1-u)*delta^(-theta))^(-1/theta) - delta);
    return (-1/b)*log1m((v/(1+v))^(1/a));
  }
}

data{
  int N;
  real y[N];
}

parameters{
  real <lower=0> a;
  real <lower=0> b;
  real <lower=0> delta;
  real <lower=0> theta;
}

model{
  for(i in 1 : N){
    y[i]~ OLGE(a, b, delta, theta);
  }
  a~ gamma(0.1, 0.1);
  b~ gamma(0.01, 0.01);
  delta~ gamma(0.2, 0.2);
  theta~ gamma(0.1, 0.1);
}

generated quantities{
  vector [N] yrep;
  for(i in 1 : N){
    yrep[i]= OLGE_rng(a, b, delta, theta);
  }
}

```

---

<div class="post-metadata">

**Author:** ![jsocolar](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/jsocolar/32/2486_2.png) [@jsocolar](https://discourse.mc-stan.org/u/jsocolar)\
**Post date:** [June 15, 2022, 1:12pm UTC](https://discourse.mc-stan.org/t/functions-block/27832/2 "2022-06-15T13:12:04Z")

</div>

A lpdf function needs to return a single real that differs by a constant from the log of the PDF; that is, it needs to compute the correct log density for its inputs. A common use case that results in the function ending with a sum is when the lpdf is vectorized over inputs corresponding to conditionally independent datapoints. In this case it is appropriate to evaluate the pointwise lpdfs and sum the result.

If the function, like yours, takes inputs of length 1, then in general no sum will be necessary or meaningful (but make sure that the function, if applied multiple times or in a loop, is applied to conditionally independent data!).

If the function takes as input vectors or arrays corresponding to data that are not conditionally independent, then it will need to compute the correct lpdf, which might include a sum, but will not correspond to the sum of some pointwise vectorized computation.

---

<div class="post-metadata">

**Author:** ![Laxmi\_Pd\_Sapkota](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/laxmi_pd_sapkota/32/11814_2.png) [@Laxmi\_Pd\_Sapkota](https://discourse.mc-stan.org/u/Laxmi_Pd_Sapkota)\
**Post date:** [June 15, 2022, 3:24pm UTC](https://discourse.mc-stan.org/t/functions-block/27832/3 "2022-06-15T15:24:25Z")

</div>

Thank you so much @jsocolar, you mean my stan codes are technically correct or there is another easy way to write up stan codes, please share if any examples like my problem.

---

<div class="post-metadata">

**Author:** ![jsocolar](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/jsocolar/32/2486_2.png) [@jsocolar](https://discourse.mc-stan.org/u/jsocolar)\
**Post date:** [June 15, 2022, 4:16pm UTC](https://discourse.mc-stan.org/t/functions-block/27832/4 "2022-06-15T16:16:03Z")

</div>

I’m not sure I understand what your question is.

- Are you wondering whether your function definition is syntactically valid (as long as it compiles then yes)?
- Are you wondering whether you are computing the lpdf correctly (I don’t know, because I don’t have any reference to the function that you are trying to compute other than the stan code that you’ve provided)?
- Are you wondering about the syntax for how to use this `_lpdf` function in the `model` block?

---

<div class="post-metadata">

**Author:** ![Laxmi\_Pd\_Sapkota](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/laxmi_pd_sapkota/32/11814_2.png) [@Laxmi\_Pd\_Sapkota](https://discourse.mc-stan.org/u/Laxmi_Pd_Sapkota)\
**Post date:** [June 16, 2022, 7:07am UTC](https://discourse.mc-stan.org/t/functions-block/27832/6 "2022-06-16T07:07:45Z")

</div>

my question is, the functions, data, parameters, model, and generated quantity blocks are syntactically valid or not? if not or is there another easy way to code up in all blocks please suggest me.  
Thanks

---

<div class="post-metadata">

**Author:** ![jsocolar](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/jsocolar/32/2486_2.png) [@jsocolar](https://discourse.mc-stan.org/u/jsocolar)\
**Post date:** [June 16, 2022, 1:16pm UTC](https://discourse.mc-stan.org/t/functions-block/27832/7 "2022-06-16T13:16:03Z")

</div>

> [@Laxmi\_Pd\_Sapkota](#):
>
> my question is, the functions, data, parameters, model, and generated quantity blocks are syntactically valid or not

The easiest way to check is to compile the model.

> [@Laxmi\_Pd\_Sapkota](#):
>
> if not or is there another easy way to code up in all blocks please suggest me

If the model doesn’t compile, the errors from the compiler will likely be informative. Post them here if you encounter them and aren’t sure what to do.

---

<div class="post-metadata">

**Author:** ![Laxmi\_Pd\_Sapkota](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/laxmi_pd_sapkota/32/11814_2.png) [@Laxmi\_Pd\_Sapkota](https://discourse.mc-stan.org/u/Laxmi_Pd_Sapkota)\
**Post date:** [June 16, 2022, 3:17pm UTC](https://discourse.mc-stan.org/t/functions-block/27832/8 "2022-06-16T15:17:04Z")

</div>

My data set is

```nohighlight
y<-c(3, 3, 8, 16, 15, 24, 26, 26, 38, 43, 46, 45, 58, 64, 66, 73, 
     73, 86, 89, 97, 108, 97, 146, 122, 143, 143, 106, 98, 136, 117, 
     121, 113, 100, 158, 81, 64, 37, 58, 65, 54, 73, 67, 85, 83, 102,
     107, 105, 228, 198, 271, 332, 353, 447, 405, 687, 642, 817, 
     972, 1079, 1356, 1625, 1629, 1873, 2381, 2388, 2791, 3271)

```

Using `rstan` package with OS windows 10,

```nohighlight
fit<- stan("OLGE_Stan.stan", iter = 400, chains = 1,  
          data = list(N=N, y=y)) 

```

I have got this type of errors, I have checked the`lpdf function` many times but couldn’t draw samples

```nohighlight
 SAMPLING FOR MODEL 'OLGE_Stan' NOW (CHAIN 1).
Chain 1: Rejecting initial value:
Chain 1: Log probability evaluates to log(0), i.e. negative infinity.
Chain 1: Stan can't start sampling from this initial value.
Chain 1: Rejecting initial value:
Chain 1: Log probability evaluates to log(0), i.e. negative infinity.
Chain 1: Stan can't start sampling from this initial value.
Chain 1: Rejecting initial value:
Chain 1: Log probability evaluates to log(0), i.e. negative infinity.
Chain 1: Stan can't start sampling from this initial value.
Chain 1: Rejecting initial value:
Chain 1: Log probability evaluates to log(0), i.e. negative infinity.
Chain 1: Stan can't start sampling from this initial value.
Chain 1: Rejecting initial value:
Chain 1: Log probability evaluates to log(0), i.e. negative infinity.
Chain 1: Stan can't start sampling from this initial value.
Chain 1: Rejecting initial value
Chain 1: Initialization between (-2, 2) failed after 100 attempts. 
Chain 1: Try specifying initial values, reducing ranges of constrained values, or reparameterizing the model.
[1] "Error in sampler$call_sampler(args_list[[i]]) : Initialization failed."
[1] "error occurred during calling the sampler; sampling not done" 

```

---

<div class="post-metadata">

**Author:** ![andrjohns](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/andrjohns/32/15297_2.png) [@andrjohns](https://discourse.mc-stan.org/u/andrjohns)\
**Post date:** [June 16, 2022, 3:52pm UTC](https://discourse.mc-stan.org/t/functions-block/27832/9 "2022-06-16T15:52:32Z")

</div>

The error is caused by these sections of your likelihood:

```stan
z = (1 - exp(-b*y))^a;
...log1m(z)...
...z/(1-z)...

```

When the `exp` function is passed values that are \< -709, the result is so small that it is treated as zero. This means that calculation for `z` then becomes: `(1 - 0)^a`, which is just `1`.

The call to `log1m(z)` then evaluates to `log(0)` and the call to `z/(1-z)` then evaluates to `1/0`

---

<div class="post-metadata">

**Author:** ![Laxmi\_Pd\_Sapkota](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/laxmi_pd_sapkota/32/11814_2.png) [@Laxmi\_Pd\_Sapkota](https://discourse.mc-stan.org/u/Laxmi_Pd_Sapkota)\
**Post date:** [June 16, 2022, 4:34pm UTC](https://discourse.mc-stan.org/t/functions-block/27832/10 "2022-06-16T16:34:42Z")

</div>

Thank you so much for your suggestion, but how to fix these issues, please suggest to me it will be a great help for this type of work in future,

---

<div class="post-metadata">

**Author:** ![jsocolar](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/jsocolar/32/2486_2.png) [@jsocolar](https://discourse.mc-stan.org/u/jsocolar)\
**Post date:** [June 16, 2022, 5:07pm UTC](https://discourse.mc-stan.org/t/functions-block/27832/11 "2022-06-16T17:07:38Z")

</div>

Do everything on the scale of log(z) using numerically stable functions.

```stan
log_z = a * log1m_exp(-b*y);
... log1m_exp(log_z) ...
... exp(log_z - log1m_exp(log_z)) ...

```

I can’t guarantee that that’ll be numerically stable enough (the last line looks ominous to me) but it’s a step in the right direction I think. Hopefully you don’t need to exponentiate the third line above and can continue to work through numerically stable log-scale functions.

---

<div class="post-metadata">

**Author:** ![jsocolar](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/jsocolar/32/2486_2.png) [@jsocolar](https://discourse.mc-stan.org/u/jsocolar)\
**Post date:** [June 16, 2022, 5:17pm UTC](https://discourse.mc-stan.org/t/functions-block/27832/12 "2022-06-16T17:17:49Z")

</div>

Ah, yes, since `delta` is constrained to be positive, you can replace `log(delta + (z/(1-z)))` with `log(delta) + log1p_exp(log_z - log1m_exp(log_z) - log(delta))`. Double check my math! But something like that anyway.

---

<div class="post-metadata">

**Author:** ![Laxmi\_Pd\_Sapkota](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/laxmi_pd_sapkota/32/11814_2.png) [@Laxmi\_Pd\_Sapkota](https://discourse.mc-stan.org/u/Laxmi_Pd_Sapkota)\
**Post date:** [June 17, 2022, 2:37am UTC](https://discourse.mc-stan.org/t/functions-block/27832/13 "2022-06-17T02:37:06Z")

</div>

My PDF is like this

f\left( {x;\Phi } \right) = \frac{{ab\delta ^\theta \theta e^{ - bx} \left( {1 - e^{ - bx} } \right)^{a - 1} }} {{\left[{1 - \left( {1 - e^{ - bx} } \right)^a } \right]^2 }}\left[{\delta + \frac{{\left( {1 - e^{ - bx} } \right)^a }} {{1 - \left( {1 - e^{ - bx} } \right)^a }}} \right]^{ - \theta - 1} ;x \> 0

where \Phi = \left( {a,b,\delta ,\theta } \right)\>0 is a vector of parameter space  
and I have supposed `z = (1 - exp(-b*y))^a` after taking log f(x) I think we could not define log of z like `log_z = a * log1m_exp(-b*y)`.in local variable. Please have a look my PDF and suggest me how to define it in function block.

As you suggest

since `delta` is constrained to be positive, you can replace `log(delta + (z/(1-z)))` with `log(delta) + log1p_exp(log_z - log1m_exp(log_z) - log(delta))` . I have run by correcting this line only but out put is same as earlier that I have post ie could not generate samples.  
thank you

---

<div class="post-metadata">

**Author:** ![jsocolar](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/jsocolar/32/2486_2.png) [@jsocolar](https://discourse.mc-stan.org/u/jsocolar)\
**Post date:** [June 17, 2022, 7:10am UTC](https://discourse.mc-stan.org/t/functions-block/27832/14 "2022-06-17T07:10:53Z")

</div>

I don’t understand what you mean when you say

> [@Laxmi\_Pd\_Sapkota](#):
>
> I think we could not define log of z like `log_z = a * log1m_exp(-b*y)`

This relationship follows directly from

> [@Laxmi\_Pd\_Sapkota](#):
>
> I have supposed `z = (1 - exp(-b*y))^a`

Given your PDF, I would take the logarithm of it and then try to simplify in such a way that we never use exponentiation directly, and instead use only things like `log1m_exp`, `log1p_exp`, `log_sum_exp` etc that are specifically written to be numerically stable. For example, after taking the logarithm the numerator of the first term becomes `log(a) + log(b) + theta * log(delta) + log(theta) - b*x + (a - 1) * log1m_exp(-b*x)`. The denominator of the first term becomes `-2 * log1m_exp(a * log1m_exp(-b * x))`. And so forth.

---

<div class="post-metadata">

**Author:** ![Laxmi\_Pd\_Sapkota](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/laxmi_pd_sapkota/32/11814_2.png) [@Laxmi\_Pd\_Sapkota](https://discourse.mc-stan.org/u/Laxmi_Pd_Sapkota)\
**Post date:** [June 17, 2022, 4:19pm UTC](https://discourse.mc-stan.org/t/functions-block/27832/15 "2022-06-17T16:19:54Z")

</div>

You are absolutely right i have written PDF as

```nohighlight
functions{
  real OLGE_lpdf(real y, real a, real b, real delta, real theta){
    real log_z;
    real w;
    log_z = a*log1m_exp(-b*y);
    w = log(a)+log(b)+ theta*log(delta)+log(theta)- b*(y) + (a-1)*(log1m(exp(-b*y)))-
  2*log1m_exp(a*log1m_exp(-b*y)) - (theta+1)*(log(delta) + log1p_exp(log_z - log1m_exp(log_z)));
  return w;
}

```

```nohighlight
fit<- stan("OLGE_Stan.stan", iter = 4000, chains = 1,  
           data = list(N=N, y=y))

```

and got the output like this

```nohighlight
Inference for Stan model: OLGE_Stan.
1 chains, each with iter=4000; warmup=2000; thin=1; 
post-warmup draws per chain=2000, total post-warmup draws=2000.

             mean se_mean sd 2.5% 25% 50% 75%
a 0.61 0.00 0.06 0.49 0.57 0.61 0.66
b 0.00 0.00 0.00 0.00 0.00 0.00 0.00
delta 0.00 NaN 0.00 0.00 0.00 0.00 0.00
theta 10.25 0.68 7.41 1.84 4.80 8.28 13.76
yrep[1] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[2] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[3] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[4] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[5] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[6] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[7] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[8] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[9] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[10] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[11] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[12] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[13] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[14] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[15] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[16] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[17] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[18] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[19] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[20] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[21] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[22] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[23] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[24] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[25] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[26] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[27] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[28] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[29] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[30] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[31] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[32] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[33] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[34] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[35] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[36] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[37] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[38] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[39] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[40] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[41] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[42] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[43] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[44] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[45] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[46] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[47] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[48] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[49] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[50] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[51] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[52] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[53] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[54] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[55] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[56] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[57] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[58] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[59] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[60] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[61] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[62] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[63] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[64] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[65] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[66] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
yrep[67] 0.00 NaN 0.00 0.00 0.00 0.00 0.00
lp__ 46672.08 0.14 1.66 46667.81 46671.34 46672.48 46673.22
            97.5% n_eff Rhat
a 0.74 817 1.00
b 0.00 129 1.04
delta 0.00 NaN NaN
theta 29.71 117 1.03
yrep[1] 0.00 NaN NaN
yrep[2] 0.00 NaN NaN
yrep[3] 0.00 NaN NaN
yrep[4] 0.00 NaN NaN
yrep[5] 0.00 NaN NaN
yrep[6] 0.00 NaN NaN
yrep[7] 0.00 NaN NaN
yrep[8] 0.00 NaN NaN
yrep[9] 0.00 NaN NaN
yrep[10] 0.00 NaN NaN
yrep[11] 0.00 NaN NaN
yrep[12] 0.00 NaN NaN
yrep[13] 0.00 NaN NaN
yrep[14] 0.00 NaN NaN
yrep[15] 0.00 NaN NaN
yrep[16] 0.00 NaN NaN
yrep[17] 0.00 NaN NaN
yrep[18] 0.00 NaN NaN
yrep[19] 0.00 NaN NaN
yrep[20] 0.00 NaN NaN
yrep[21] 0.00 NaN NaN
yrep[22] 0.00 NaN NaN
yrep[23] 0.00 NaN NaN
yrep[24] 0.00 NaN NaN
yrep[25] 0.00 NaN NaN
yrep[26] 0.00 NaN NaN
yrep[27] 0.00 NaN NaN
yrep[28] 0.00 NaN NaN
yrep[29] 0.00 NaN NaN
yrep[30] 0.00 NaN NaN
yrep[31] 0.00 NaN NaN
yrep[32] 0.00 NaN NaN
yrep[33] 0.00 NaN NaN
yrep[34] 0.00 NaN NaN
yrep[35] 0.00 NaN NaN
yrep[36] 0.00 NaN NaN
yrep[37] 0.00 NaN NaN
yrep[38] 0.00 NaN NaN
yrep[39] 0.00 NaN NaN
yrep[40] 0.00 NaN NaN
yrep[41] 0.00 NaN NaN
yrep[42] 0.00 NaN NaN
yrep[43] 0.00 NaN NaN
yrep[44] 0.00 NaN NaN
yrep[45] 0.00 NaN NaN
yrep[46] 0.00 NaN NaN
yrep[47] 0.00 NaN NaN
yrep[48] 0.00 NaN NaN
yrep[49] 0.00 NaN NaN
yrep[50] 0.00 NaN NaN
yrep[51] 0.00 NaN NaN
yrep[52] 0.00 NaN NaN
yrep[53] 0.00 NaN NaN
yrep[54] 0.00 NaN NaN
yrep[55] 0.00 NaN NaN
yrep[56] 0.00 NaN NaN
yrep[57] 0.00 NaN NaN
yrep[58] 0.00 NaN NaN
yrep[59] 0.00 NaN NaN
yrep[60] 0.00 NaN NaN
yrep[61] 0.00 NaN NaN
yrep[62] 0.00 NaN NaN
yrep[63] 0.00 NaN NaN
yrep[64] 0.00 NaN NaN
yrep[65] 0.00 NaN NaN
yrep[66] 0.00 NaN NaN
yrep[67] 0.00 NaN NaN
lp__ 46674.11 137 1.00

```

Still there is problem, what is happen

---

<div class="post-metadata">

**Author:** ![jsocolar](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/jsocolar/32/2486_2.png) [@jsocolar](https://discourse.mc-stan.org/u/jsocolar)\
**Post date:** [June 17, 2022, 4:38pm UTC](https://discourse.mc-stan.org/t/functions-block/27832/16 "2022-06-17T16:38:11Z")

</div>

It looks like the model is working fine, but there’s still an underflow problem in the RNG and therefore in the generated quantities.

---

<div class="post-metadata">

**Author:** ![Laxmi\_Pd\_Sapkota](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/laxmi_pd_sapkota/32/11814_2.png) [@Laxmi\_Pd\_Sapkota](https://discourse.mc-stan.org/u/Laxmi_Pd_Sapkota)\
**Post date:** [June 18, 2022, 3:38pm UTC](https://discourse.mc-stan.org/t/functions-block/27832/17 "2022-06-18T15:38:28Z")

</div>

The RNG that I have written as

```nohighlight
real OLGE_rng(real a, real b, real delta, real theta){
    real u;
    real log_v;
    u = uniform_rng(0, 1);
    log_v = log(-delta)+ log1p(exp((-1/theta)*(log1m(u)-
    theta*log(delta)))- log(-delta));
    return (-1/b)*(log1m_exp((1/a)*(log_v - log1p_exp(log_v))));

```

and my actual Quantile function is  
Q\left( p \right) = - \frac{1} {b}\left[{\log \left\{ {1 - \left( {\frac{v} {{1 +v}}} \right)^{1/a} } \right\}} \right]

where v = \left[{\left\{ {\left( {1 - p} \right)\delta ^{ - \theta } } \right\}^{ - 1/\theta } - \delta } \right]  
is my RNG function is correct according to this?

after compiling with this RNG function I got the same result as earlier

```nohighlight
1 chains, each with iter=2000; warmup=1000; thin=1; 
post-warmup draws per chain=1000, total post-warmup draws=1000.

             mean se_mean sd 2.5% 25% 50% 75%
a 0.62 0.01 0.07 0.50 0.57 0.62 0.66
b 0.00 0.00 0.00 0.00 0.00 0.00 0.00
delta 0.00 NaN 0.00 0.00 0.00 0.00 0.00
theta 9.70 1.50 6.66 2.28 4.93 7.83 12.52
yrep[1] NaN NA NA NA NA NA NA
yrep[2] NaN NA NA NA NA NA NA
yrep[3] NaN NA NA NA NA NA NA
yrep[4] NaN NA NA NA NA NA NA
yrep[5] NaN NA NA NA NA NA NA
yrep[6] NaN NA NA NA NA NA NA
yrep[7] NaN NA NA NA NA NA NA
yrep[8] NaN NA NA NA NA NA NA
yrep[9] NaN NA NA NA NA NA NA
yrep[10] NaN NA NA NA NA NA NA
yrep[11] NaN NA NA NA NA NA NA
yrep[12] NaN NA NA NA NA NA NA
yrep[13] NaN NA NA NA NA NA NA
yrep[14] NaN NA NA NA NA NA NA

```

---

<div class="post-metadata">

**Author:** ![andrjohns](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/andrjohns/32/15297_2.png) [@andrjohns](https://discourse.mc-stan.org/u/andrjohns)\
**Post date:** [June 18, 2022, 4:35pm UTC](https://discourse.mc-stan.org/t/functions-block/27832/18 "2022-06-18T16:35:11Z")

</div>

Your RNG is attempting to take the log of a negative number:

```nohighlight
log(-delta)

```

Which returns `NaN` and causes the final result to also be `NaN`

---

<div class="post-metadata">

**Author:** ![Laxmi\_Pd\_Sapkota](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/laxmi_pd_sapkota/32/11814_2.png) [@Laxmi\_Pd\_Sapkota](https://discourse.mc-stan.org/u/Laxmi_Pd_Sapkota)\
**Post date:** [June 19, 2022, 2:33am UTC](https://discourse.mc-stan.org/t/functions-block/27832/19 "2022-06-19T02:33:13Z")

</div>

I have just correct the Rng function as suggested by @andrjohns  
`log(-delta)` returns NAN.

```nohighlight
real OLGE_rng(real a, real b, real delta, real theta){
    real u;
    real log_v;
    u = uniform_rng(0, 1);
    log_v = log_diff_exp((-1/theta)*(log1m(u)-
    theta*log(delta)), log(delta));
    return (-1/b)*(log1m_exp((1/a)*(log_v - log1p_exp(log_v))));

```

but still get that same output as earlier

---

<div class="post-metadata">

**Author:** ![andrjohns](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/andrjohns/32/15297_2.png) [@andrjohns](https://discourse.mc-stan.org/u/andrjohns)\
**Post date:** [June 19, 2022, 12:17pm UTC](https://discourse.mc-stan.org/t/functions-block/27832/20 "2022-06-19T12:17:53Z")

</div>

You’ll need to do some debugging and testing to see where in your RNG the error is occurring. Try breaking the calculation into separate parts and seeing which part is returning `NaN`. You can also add `print()` statements to have Stan print out the values of particular variables/computations during sampling