Sas random exponential

The POISSON function returns the probability that an observation from a Poisson distribution, with mean m , is less than or equal to n. The forecasts from exponential smoothing are The models for the response variable consist of a linear effect composed of the covariates and a random disturbance term. The ** operator is the correct answer. NumSamples = 10; /* number of samples */. I think I did it correctly, but I cannot find anything on the internet to verify my code. Normal, Poisson, exponential—these and other "named" distributions are used daily by statisticians for modeling and analysis. Function Compatibility with SBCS, DBCS, and MBCS Character Sets. 5 Poisson Regression. Notice that only a transaction data set exists. 14 Piecewise Exponential Frailty Model. Individual growth models are designed for exploring longitudinal data on individuals over time. However, if the start or end of the input series does not correspond to the start or end of an output interval, some output A generalized linear mixed model (GLMM) is an extension of the generalized linear model (GLM) in which the linear predictor contains random effects in addition to the usual fixed effects. The examples are easily extendable to more sophisticated situations. Prior to SAS 9. or expression that specifies a random variable. Feel free to leave out the streaminit() function to produce a different random value each time you run the code. Conditional on the random effects, data have distributions in the For simplicity, I will demonstrate how to generate a random integer between 1 and 10. 1) Expoentiatl with scale parameter sigma=0. 7423, on the basis of the following code: Jan 10, 2022 · This means that each time we run this code, the random number will be 9. To be consistent with the standard informat, ROUND(0. These models can take various forms, but the most common ones involve a conditional distribution for the response variable given the random effects. For example, let Xbe a Bernoulli random variable that takes on the The following SAS statements represent one way of doing this: proc mixed data=rc; class Batch Monthc; model Y = Month / s; random Int Month Monthc / sub=Batch s; run; The variable Monthc is added to the CLASS and RANDOM statements, and it models the nested errors. 1) go to the log. The mean parameters found when fitting an exponential mixture model to the standard-stay group and the long-stay group are 619 and 7752 days, respectively. Aug 1, 2017 · By using SEVERITY procedure, I found that the exponential distribution is the one that fits better empirical data; so, I got the parameter theta. There are four operations that are used often when you work with statistical distributions. As in the GLM procedure, LS-means are predicted population margins —that is, they estimate the marginal means over a balanced population. Below, I have written a small SAS program that lets you set the shape parameter and scale parameter and plot the corresponding Gamma probability density function. An exponential variate X with parameter LAMBDA can be generated: x=ranexp(seed)/lambda; An extreme value variate X with location parameter ALPHA and scale Table B. RANNOR* Details. 5, Weibull_Scale=2300, Weibull_Shape=0. An exponential variate X with parameter LAMBDA can be generated: x=ranexp(seed)/lambda; An extreme value variate X with location parameter ALPHA and scale learn how to use the SAS/IML language effectively, see Wicklin (2010). 10: ods graphics on; proc mcmc data=input outpost=postout nmc=50000 thin=5 seed=7893 plots=trace; ods select Parameters REparameters PostSummaries PostIntervals. Here is the code I have started: PROC IML; research studies use highly simplified models, such as the exponential, that do not adequately reflect the patterns of time to event and censoring seen in real datasets. The orginal normal distribution has a mean of 38 and standard of 5. The rate parameter is an alternative, widely used Jan 29, 2018 · The new random-number generators in SAS provide analysts with fast, high-quality, state-of-the-art random numbers. The SET statement with the POINT= option then uses random access to select the kth observation. The RAND function generates random numbers from various continuous and discrete distributions. The EXP function applies the exponential function to every element of the argument matrix. exponential () method, we are able to get the random samples of exponential distribution and return the samples of numpy array. In a sense, LS-means are to unbalanced designs as class and subclass arithmetic means are to balanced designs. The SAS mitigateBias uses a highly versatile approach (exponential gradient reduction) that: Applies to any classifier family Allows many definitions of fairness, including demographic parity and equalized odds The a How PROC MCMC Works. The result parameter should be preallocated to a size equal to the The RAND function returns at most 2 32 distinct values. effect name < effect values …>. First, let us generate a random number between 1 and 10. If you decide to pursue the exponential model, you might not need to use NLMIXED. Not sure why this got two upvotes, but it's incorrect; there is no POWER function in base SAS, unless you implement it yourself. In order to add an overdispersion component to the variance function, simply specify a single residual random component. 1 User’s Guide. d v. An inverse transform method applied to a RANUNI uniform variate is used. The default sampling methods include conjugate sampling (from full conditional), direct sampling from the marginal distribution, inverse cumulative distribution function, random walk Metropolis with normal A generalized linear mixed model (GLMM) is an extension of the generalized linear model (GLM) in which the linear predictor contains random effects in addition to the usual fixed effects. Syntax. and solve for the root of f. By default, PROC PHREG examines the relative change in the variance estimate between optimizations (see the PCONV= option). 7, Scale=4. Using Functions and CALL Routines. Example 2. SAS® 9. Nov 11, 2017 · Random Number Generating. 2) copy the generated data step code to the editor. The forecasts from exponential smoothing are Sep 5, 2012 · It is because different SAS functions were called to generate the streams of random number, which results in the differences of derived sample sizes. Part of the notation and presentation in this example follows Clayton and the Luek example in Spiegelhalter et al. Generally speaking, the proportional hazards model assumes the hazard function, Mar 16, 2017 · The RAND function generates random numbers from various continuous and discrete distributions. data test; do i=1 to 100; ran_num=ceil(ranuni(1)*18); output; end; Details. Aitkin et al. Another option is use the Data menu in Excel to do a Text to Column conversion on the numeric column prior to importing (ensure you select column type Text during in the Wizard). Examples include population growth, the height of a child, and the growth of a tumor cell. 16 uses the same data set as Example 71. School administrators study the attendance behavior of high school juniors at two schools. The following code shows how to generate a variable in SAS that contains 10 random values between 1 In probability theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the distance between events in a Poisson point process, i. random. Most of the terminology in this book is standard. Example 1. RANCAU* returns a random variate from a Cauchy distribution . 01 ; Details. The LSMEANS statement computes least squares means (LS-means) of fixed effects. 9 and Figure 55. I also looked online to see compatible distribution for the Rand function but non specify the Oct 2, 2019 · It is a mathematical fact that the geometric mean of data is always less than the arithmetic mean. This course discusses the fundamentals of modeling time series data. The basic techniques include the (1) inverse probability transform and other transformations, (2) composition method, and (3) acceptance-rejection methods. @Joe, power() is valid in proc ds2 now. This distribution is either a member of the exponential family of distributions or one of the supplementary distributions provided by the GLIMMIX procedure. Examples of negative binomial regression. The deviance information criterion (DIC) is used to do model selections, and you can also find programs that visualize posterior quantities. com. The expected number of duplicates in a random uniform sample of size M is approximately M 2 /2 33 when M is much less than 232. ( − x β), for x > 0 and 0 elsewhere. Consider the Rats data set in the section Getting Started: PHREG Procedure. Select the transaction data set and click Browse. The lower bound of an exponential r. Using Random-Number Functions and CALL Routines. If you want to create reproducible streams of random numbers, then specify CALL STREAMINIT before any calls to the RAND random number function. PROC FORECAST can fit three types of time trend models: constant, linear, and quadratic. In these examples, the distribution and parameter names in the string value are the names that are used in the Theoretical Oct 9, 2017 · - The random variable E/lambda is exponential with rate parameter lambda. 0, size=None) #. 9: Exponential Distribution Parameter Names. However, a term that you might not be familiar with is the term random variate. From SAS 9. If exponential and square root refer to your model equation, i. This example shows you how to use PROC MCMC to analyze the treatment effect for the E1684 melanoma clinical trial data. A Random Integer Between 1 and 10. 4M5, SAS supported the Mersenne twister random-number generator (introduced in SAS 9. SAS/STAT® 15. • If the model contains random effects, the distribution of the data conditional on the random effects is known. Note that Month and Monthc are continuous and classification versions of the same random. An exponential variate X with parameter LAMBDA can be generated: x=ranexp (seed)/lambda; x=ranexp(seed)/lambda; An extreme value variate X with location Oct 27, 2018 · The random functions create a value between 0 and 1. Nov 16, 2016 · Re: Excel import - Exponential value into SAS as character field. Its probability density function is. Growth curves model the evolution of a quantity over time. The 20th SAS Simulation Studio 15. Customer Support SAS Documentation. The CALL RANEXP routine uses an inverse transform Jul 21, 2021 · First I ran PROC LIFEREG with the following model statement: MODEL day*cnsr (1)= / dist=Weibull; This generated the following ML estimates: Intercept=7. 4 TS level 1M3 on Microsoft windows 10 enterprise (x64), I couldn’t get the same result. 2 because that value is used in Bono, et al. The model you state is a generalized linear model with a log link function: model MWT = years / dist=normal link=log; Example 54. The RANEXP function returns a variate that is generated from an exponential distribution with parameter 1. 1) computes the result as 3/10, and the following statement produces the results that you would expect. I think you do not need the 8. data Exponential_PDF; do x = 0 to 4 by 0. The mixture distribution fits the data better than the exponential distribution, especially at the low values of LOS. Suppose the following hypothetical insurance claims data are classified by two factors: age group (with two levels) and car SAS Customer Support Site | SAS Support Sep 16, 2015 · An alternative model is to fit an OLS model for log (Y). Conditional on the random effects, data have distributions in the Dec 7, 2023 · The single-component exponential model had an average LOS of 3712 days. returns a random variate from a specified distribution. Below a code sample using ranuni (). The random number generator has a very long period (2 Jan 19, 2016 · 1. But the mean sample size under the Weibull distribution with of 1, which was estimated from 10 simulations with the same seeds as the simulations of the exponential distribution, is 601. In a random uniform sample of size 10 5, the chance of drawing at least one duplicate is greater than 50%. Here is my code: Well, rexp is using rate as second parameter, and mean=1/rate, so rexp(100, 1. The following examples show (case-sensitive) string values that can be used as Numeric Source block DataStreamDescription factor values or InStreamPolicy port values. The following elements can appear in the ESTIMATE statement: 'label'. You can initialize the random number stream that is used by RANDGEN by calling the RANDSEED subroutine. Exponential smoothing fits a time trend model by using a smoothing scheme in which the weights decline geometrically as you go backward in time. 1) and a hardware-based RNG (supported on Intel CPUs in SAS 9. The exponential is the natural number raised to the indicated power. PROC MIXED allows the growth parameters for each individual to be examined as random effects in the model. The variance function is replaced by : proc glimmix; model count = x x*x / dist=poisson; Then you simply need to sample from a (shifted) truncated exponential appropriate to that segment. 3 Functions and CALL Routines. 22. This article shows how to use SAS to fit a growth curve to data. These data were collected to assess the effectiveness of using interferon alpha-2b in chemotherapeutic treatment of melanoma. Use the rand() function with the 'exponential' argument; however, if you want between 9% and 14% of the values to be < 1, you'll need to solve for Lambda using the formula for the CDF of the exponential distribution. exponential(scale=1. To understand the steps involved in each of the proofs in the lesson. I built a random dataset distributed according to an exponential distribution wiith parameter theta equal to 0. Between these two examples, you will learn several methods to fit a multivariate The following statements fit a linear random-effects model to the data and produce the output shown in Figure 55. 3" appear as a constant in a SAS program, the value is computed by the standard informat as 3/10. Minimum value is 30 maximum value is 50. These are nicely summarized in Rubinstein (1981). (See the RANDGEN subroutine. Personally, just to save time, I would simulate some values of Lambda and select the one that fits the criteria. 8. The RAND function uses the Mersenne-Twister random number generator (RNG) that was developed by Matsumoto and Nishimura (1998). Simply use the SUBJECT= option to define returns a random variate from a binomial distribution . You can use the Poisson distribution to model the distribution of cell counts in a multiway contingency table. Jul 19, 2017 · The first thing you should do is graph your data: I don't see any evidence of an exponential behavior. v. Subsequent calls to the RAND function generate a stream of pseudorandom variates from a specified probability distribution by using the specified RNG. 5 Programming Documentation PROC FORECAST can fit three types of time trend models: constant, linear, and quadratic. 3 User's Guide documentation. The e-learning format of this course Jan 18, 2016 · The aim is to simulate a truncated [a=30,b=50] distribution that is normally distribution. 5. The resampling process should respect the null hypothesis or reflect the original sampling scheme. Example 73. A root is found in (-infinity, 0) or (0,infinity), depending on the values of the parameters. SAS Functions and CALL Routines. In the following DATA step, the RAND function generates a random integer k in the range 1; N , where N is the number of observations in a data set. Classification, or CLASS, variables can be used as effects, and indicator variables are generated for the class levels. 1: User's Guide documentation. e. The curves fit by PROC EXPAND should not be used for forecasting. The distribution of the random disturbance can be taken from a class of distributions that includes the extreme value, normal, logistic, and, by using a log transformation, the exponential, Weibull, lognormal, loglogistic The NLMIXED procedure fits nonlinear mixed models, that is, models in which both fixed and random effects are permitted to have a nonlinear relationship to the response variable. PROC EXPAND normally avoids extrapolation of values beyond the time range of the nonmissing input data for a series, unless the EXTRAPOLATE option is used. Use the POWER function and, if necessary, the CONSTANT function. 0, size=None) Return : Return the random samples of numpy array. 0) probably SAS Code Gamma Example. The above case is aimed to generate on one instance Nov 20, 2023 · This blog will do a deeper dive on the mitigateBias action and how to tune it. Oct 19, 2011 · By Rick Wicklin on The DO Loop October 19, 2011. Following generation,I like to check to see that the generated distribution is in fact a PDF. Here are the steps you can take to create a new probability distribution: Choose any nonnegative, piecewise continuous, integrable function, w, on a finite or infinite domain, D ⊆ R. This example covers two commonly used survival analysis models: the exponential model and the Weibull model. Individual-level covariates can be entered into the model as fixed effects to determine their impact on the dependent variable alone and in distribution for your data (given the random effects) having either a standard form (normal, binomial, Poisson) or a general distribution that you code using SAS programming statements. The random number generator has a very long period (2 Example 52. This article focuses on using PROC NLIN to estimate the parameters in a nonlinear least squares model. Nonnegative means that w ( x) ≥ 0 for all x in D. Jul 22, 2013 · The following DATA step generates random values from the exponential distribution by generating random uniform values from U(0,1) and applying the inverse CDF of the exponential distribution. Consequently, I encourage you to copy/paste this code into your editor and familiarize yourself with how the shape and scale parameters affect the distribution. For other kinds of trend models, other SAS procedures can be used. Obviously f (0) > 0, so x=0 is never a root of f. We do so in the simplest possible way. If the characters "0. PG. 2. GLMMs also inherit from GLMs the idea of extending linear mixed models to nonnormal data. Jun 16, 2015 · PROC GENMOD and PROC GLIMMIX can fit models where the response is assumed to possess a probability distribution of the exponential form. Oct 21, 2009 · 1. New random-number generators in SAS. Wherever possible, the simplest form of the distribution is used. In this article, I present a general method of simulating such data based on flexible parametric survival models (Royston and Parmar, 2002, Statistics in Medicine 21: 2175 Dec 12, 2018 · In general, the basic bootstrap method consists of four steps: Compute a statistic for the original data. /50. The model assumes that the errors are normally distributed and that the expected value of log (Y) is linear: E (log (Y)) = b 0 + b 1 X. SAS Code Example. The course focuses on the applied use of the three main model types used to analyze univariate time series: exponential smoothing, autoregressive integrated moving average with exogenous variables (ARIMAX), and unobserved components (UCM). In SAS software, the operations are available by using the following four Example 64. 4 and SAS® Viya® 3. The CALL RANEXP routine updates seed and returns a variate x that is generated from an exponential distribution that has a parameter of 1. (2020). The REPEATED statement is used to specify the matrix in the mixed model. To learn key properties of an exponential random variable, such as the mean, variance, and moment generating function. A repeated measures analysis can be done using a log-linked generalized linear model as you suggest either with PROC MIXED (if Y is normal) or PROC GLIMMIX. f ( x; 1 β) = 1 β exp. For example, the following statements fit a polynomial Poisson regression model with overdispersion. For many repeated measures models, no repeated effect is required in the REPEATED statement. , a process in which events occur continuously and independently at a constant average rate; the distance parameter could be any meaningful mono-dimensional measure of the process, such as time Uniform generators may be used to create streams of pseudo-random numbers that have other distributions. 2) Gamma with shape parameter alpha=2 and shape parameter sigma=0. I want to store these numbers in a vector. An additional model parameter, s2, the variance of the random-effects parameters, is needed for the model. is 0, so adding 1 would translate the threshold to 1. ) RANEXP* returns a random variate from an exponential distribution . For example, you should expect about 115 duplicates in Aug 2, 2015 · There are many parameterization of distribution functions, but it sounds like you want. ⁡. Predictors of the number of days of absence include the type of program in which the student is enrolled and a standardized test in math. Jul 31, 2023 · How to create a probability distribution. What's New in SAS 9. An estimate-specification takes the general form. (Of course, the simpler way is to use x = RAND("Expo")!) The UNIVARIATE procedure is used to check that the data follow an exponential distribution. The CDF function for the Normal distribution returns the probability that an observation from the Normal distribution, with the location parameter θ and the scale parameter λ, is less than or equal to x . Using R, I want to generate 100 random numbers from an exponential distribution with a mean of 50. SAS® Help Center. RANGAM* returns a random variate from a gamma distribution . Syntax : numpy. Exponential and Weibull models are widely used for survival analysis. The results are not shown here. ( 1989) have used this method to model insurance claims data. The PHREG procedure applies this criterion to the variance parameter estimate of the random effects. If you do that SAS will read the column as character. If you call the RAND function before you specify a seed with the CALL STREAMINIT routine (or if you specify a nonpositive seed value in the CALL STREAMINIT routine), then the RAND function uses Jul 15, 2020 · exponential distribution. For example, the following statements compute the exponentials of several numbers: Apr 27, 2020 · I would suggest that if you used Proc Import to read the data that you do so again but afterward. Then, to simulate time values in a new huge dataset, I used the SAS statements: Oct 10, 2018 · 3. The STREAMINIT subroutine uses an initial-seed value to initialize a random-number generator. The OLS model assumes that log (Y) is predicted by a model of the form b 0 + b 1 X + ε. tracepanel; For example, the following statement generates starting values in these steps: proc glimmix method=quad(initpl=5); A GLM without random effects is fit initially to obtain as starting values for the fixed effects. Feb 23, 2018 · f (x) = D0^x - D1^x + D2^x. Definitions of Functions and CALL Routines. exponential (scale=1. The choice of the quantile, p, is arbitrary, but I will use p=0. Examples of three valid MODEL statements follow: a: model time*flag(1,3)=temp; b: model (start, finish)=; c: model r/n=dose; The basic element of the ESTIMATE statement is the estimate-specification, which consists of model effects and their coefficients. If no REPEATED statement is specified, is assumed to be equal to . Two outliers, the observations in rows 61 and 70, are replaced with their predicted values in the Time Series ID: 2 series. May 17, 2024 · Re: Exponential decay model with repeated measurements. In models without random effects, Jan 1, 2007 · INTRODUCTION Exponential random graph modeling (ERGM, also known as p-star) is a statistical technique for modeling structural properties of networks (Snijders, Pattison, Robins, & Handcock, 2004). The equation follows: C D F ( ′ N O R M A L ′ , x , θ , λ ) = 1 λ 2 π ∫ - ∞ x e ( - ( v - θ ) 2 2 λ 2 ) ⁢. 4M3). com SAS® Help Center CDF Exponential Distribution Function. The SAS code below lets you set and draw the probability density function for the corresponding exponential function. If you want a truncated exponential distribution, you would use an IF-THEN statement to accept/reject the random values in [1,8], such as Table B. 3) modify any informat/format statements to make sure that the variables are read as the correct type and with an appropriate length. Example #1 : In this example we can see that by using numpy. Familiarize yourself with the impact of on the shape of the density. By adjusting the seeds, you can force streams of variates to agree or disagree for some or all of the observations in the same, or in subsequent, DATA steps. 4 Functions and CALL Routines: Reference, Fifth Edition documentation. RAND . . Example 59. If you want values between 1 - 18 then just multiply the value by 18 and then use the ceil () function to shift the result to the next higher integer. You can generate 5 x 10 = 50 observations as follows: proc iml; N = 5; /* size of each sample */. May 22, 2024 · I am working with a study where we expect an exponential decay relationship between increasing dose and a pharmacodynamic response variable of interest. In these examples, the distribution and parameter names in the string value are the names that are used in the Theoretical Jan 18, 2024 · Details. 4 DS2 Language Reference, PDF EXPONENTIAL Distribution Function. Its syntax is different from that of the REPEATED statement in PROC GLM. Suppose denotes the estimate of the variance parameter at the th optimization. The RANDGEN subroutine generates random numbers by using the same numerical method as the RAND function in Base SAS software, with the efficiency optimized for matrices. Another approach is a Generalized Estimating Equations model using PROC GEE which doesn't involve introducing any random effects. For the first few observation in your data set, the roots occur for x<0, as shown by the following graph. The INITITER= option in the PROC GLIMMIX statement controls the number of iterations in this step. To compute the geometric mean and geometric CV, you can use the DIST=LOGNORMAL option on the PROC TTEST statement, as follows: proc ttest data =Have dist=lognormal; var x ; Jul 29, 2017 · 2. 14 Bayesian Analysis of Piecewise Exponential Model. 11 Analysis of Clustered Data under The PHREG Procedure in SAS/STAT® 13. I encourage you to play around with this code. 7 Exponential and Weibull Survival Analysis. 4M5, the Rand Function supports the ‘Integer Nov 4, 2020 · The expected value in the tail of the exponential distribution. and I am asked to generate 10,000 random numbers using the Inversion Method for Cauchy Distribution. 4) Save the code. Posted 11-11-2017 05:52 PM (1168 views) I'm given these two equations: PDF: f (x) =1/ (π (1+x^2)) -∞ ≤ x ≤ ∞ CDF: F (x) = (1/2) + arctan (x)/π -∞ ≤ x ≤ ∞. Apr 10, 2013 · Now suppose that you want to generate 10 samples, where each sample contains five observations from a trivariate normal distribution. PROC NLMIXED fits nonlinear mixed models by maximizing an approximation to the likelihood integrated over the random effects. If you do not specify any covariates following the equal sign, an intercept-only model is fit. 16 Piecewise Exponential Frailty Model under The MCMC Procedure in SAS/STAT® 13. There are a variety of approaches for the truncated exponential, depending on your needs (speed, ease of generation, any known facts about the likely width of the interval relative to the mean of the untruncated exponential, and so on). β is the scale parameter, which is the inverse of the rate parameter λ = 1 / β . PROC MCMC is a simulation-based procedure that applies a variety of sampling algorithms to the program at hand. About This Book. Draw samples from an exponential distribution. Jul 29, 2019 · In the SAS learning course Programming 2, the rand function was used with “Integer” for random values to the data but when I tried it using my SAS 9. This example illustrates how to fit a piecewise exponential frailty model using PROC MCMC. To compute the probability that an observation is equal to a given value, n, compute the difference of two probabilities from the Poisson distribution for n and n -1. Python3. The data set already contains a variable called LogY = log (Y). This example illustrates using a piecewise exponential model in a Bayesian analysis. you are trying to fit a non-linear model, then PROC NLIN will likely accomodate your needs. Use the DATA step or PROC SURVEYSELECT to resample (with replacement) B times from the data. To learn a formal definition of the probability density function of a (continuous) exponential random variable. Details. com Mar 18, 2020 · Select the ellipses next to the Exported Data property for the TS Exponential Smoothing node. For these data, the geometric mean is 20. Using SYSRANDOM and SYSRANEND Macro May 13, 2024 · The RAND function works with the STREAMINIT and STREAM subroutines. An initial idea was therefore to model this using an exponential regression model on the form A second RANDOM statement defines a subject-level random effect u, and the random-effects parameters enter the model in the term for the regression mean, bZ. The purpose of the ABSPCONV= criterion is Dec 13, 2023 · SAS® 9. data findLambda; a random sampling scheme by using the RAND function in the DATA step. 5; For both situations you can allocate a vector (or matrix) and fill it up by calling the RANDGEN subroutine. For an example, let's look at the exponential distribution. Example 2: Generate Variable with Several Random Numbers. 33,0. The exponential distribution is defined only for x ≥ 0, so the left tail starts a 0. Although there are several families of copulas, this article focuses on the Gaussian copula, which is the simplest to understand. sas. In the following statements, PROC PHREG is used to carry out a Bayesian analysis for the piecewise exponential model. A random variate is a particular outcome of a random variable (Devroye 1986). Jul 5, 2021 · The literature for copulas is mathematically formidable, but this article provides an intuitive introduction to copulas by describing the geometry of the transformations that are involved in the simulation process. az dl hw oh ct ir zx ah ei ag