Problem Note 64711: RAND function with BINOMIAL distribution and RANBIN function might return poor results if "n" is large
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The RAND(‘BINOMIAL’, p, n) function and the RANBIN(seed, n, p) function might return pseudo-random variates that do not adequately follow the Binomial distribution if n is large and p approaches 0 or 1.
Under the following conditions, a Normal approximation to the Binomial distribution is used by the RAND and RANBIN functions:
- n > 300, and
- (n*p) > 5, and
- (n*(1-p)) > 5
Otherwise, the Inverse Transform method is used. The Normal approximation to the Binomial distribution does not perform well when p approaches 0 or 1.
To circumvent the problem when n > 300, you can compute the sum of several Binomial random variates with n ≤ 300. For example, instead of specifying:
X=Rand(‘BINOMIAL’, p, 700);
you can run the equivalent code below to define your Binomial random variable, X:
X1=Rand(‘BINOMIAL’, p, 300);
X2=Rand(‘BINOMIAL’, p, 300);
X3=Rand(‘BINOMIAL’, p, 100);
X = X1+X2+X3;
Note: This behavior is observed under the aforementioned conditions with the RAND(‘BINOMIAL’, p, n) function for all of the random-number generators supported in the CALL STREAMINIT<(RNG, seed)>; subroutine.
Operating System and Release Information
| Product Family | Product | System | SAS Release | |
| Reported | Fixed* | |||
| SAS System | Base SAS | z/OS | ||
| z/OS 64-bit | ||||
| OpenVMS VAX | ||||
| Macintosh | ||||
| Microsoft® Windows® for 64-Bit Itanium-based Systems | ||||
| Microsoft Windows Server 2003 Datacenter 64-bit Edition | ||||
| Microsoft Windows Server 2003 Enterprise 64-bit Edition | ||||
| Microsoft Windows XP 64-bit Edition | ||||
| Microsoft® Windows® for x64 | ||||
| OS/2 | ||||
| Microsoft Windows 8 Enterprise 32-bit | ||||
| Microsoft Windows 8 Enterprise x64 | ||||
| Microsoft Windows 8 Pro 32-bit | ||||
| Microsoft Windows 8 Pro x64 | ||||
| Microsoft Windows 8.1 Enterprise 32-bit | ||||
| Microsoft Windows 8.1 Enterprise x64 | ||||
| Microsoft Windows 8.1 Pro 32-bit | ||||
| Microsoft Windows 8.1 Pro x64 | ||||
| Microsoft Windows 10 | ||||
| Microsoft Windows 95/98 | ||||
| Microsoft Windows 2000 Advanced Server | ||||
| Microsoft Windows 2000 Datacenter Server | ||||
| Microsoft Windows 2000 Server | ||||
| Microsoft Windows 2000 Professional | ||||
| Microsoft Windows NT Workstation | ||||
| Microsoft Windows Server 2003 Datacenter Edition | ||||
| Microsoft Windows Server 2003 Enterprise Edition | ||||
| Microsoft Windows Server 2003 Standard Edition | ||||
| Microsoft Windows Server 2003 for x64 | ||||
| Microsoft Windows Server 2008 | ||||
| Microsoft Windows Server 2008 R2 | ||||
| Microsoft Windows Server 2008 for x64 | ||||
| Microsoft Windows Server 2012 Datacenter | ||||
| Microsoft Windows Server 2012 R2 Datacenter | ||||
| Microsoft Windows Server 2012 R2 Std | ||||
| Microsoft Windows Server 2012 Std | ||||
| Microsoft Windows Server 2016 | ||||
| Microsoft Windows Server 2019 | ||||
| Microsoft Windows XP Professional | ||||
| Windows 7 Enterprise 32 bit | ||||
| Windows 7 Enterprise x64 | ||||
| Windows 7 Home Premium 32 bit | ||||
| Windows 7 Home Premium x64 | ||||
| Windows 7 Professional 32 bit | ||||
| Windows 7 Professional x64 | ||||
| Windows 7 Ultimate 32 bit | ||||
| Windows 7 Ultimate x64 | ||||
| Windows Millennium Edition (Me) | ||||
| Windows Vista | ||||
| Windows Vista for x64 | ||||
| 64-bit Enabled AIX | ||||
| 64-bit Enabled HP-UX | ||||
| 64-bit Enabled Solaris | ||||
| ABI+ for Intel Architecture | ||||
| AIX | ||||
| HP-UX | ||||
| HP-UX IPF | ||||
| IRIX | ||||
| Linux | ||||
| Linux for x64 | ||||
| Linux on Itanium | ||||
| OpenVMS Alpha | ||||
| OpenVMS on HP Integrity | ||||
| Solaris | ||||
| Solaris for x64 | ||||
| Tru64 UNIX | ||||
| Type: | Problem Note |
| Priority: | high |
| Topic: | Analytics ==> Distribution Analysis Analytics ==> Simulation SAS Reference ==> Functions ==> Random Number ==> CALL RANBIN SAS Reference ==> Functions ==> Random Number ==> CALL STREAMINIT SAS Reference ==> Functions ==> Random Number ==> RANBIN SAS Reference ==> Functions ==> Random Number ==> RAND |
| Date Modified: | 2019-09-04 15:44:19 |
| Date Created: | 2019-08-29 14:40:20 |