EM Algorithm for Mixtures of Gamma Distributions

Return EM algorithm output for mixtures of gamma distributions.

Usage

gammamixEM(x, lambda = NULL, alpha = NULL, beta = NULL, k = 2,
           mom.start = TRUE, fix.alpha = FALSE, epsilon = 1e-08, 
           maxit = 1000, maxrestarts = 20, verb = FALSE)

Arguments

x

A vector of length n consisting of the data.

lambda

Initial value of mixing proportions. If NULL, then lambda is random from a uniform Dirichlet distribution (i.e., its entries are uniform random and then it is normalized to sum to 1).

alpha

Starting value of vector of component shape parameters. If non-NULL, alpha must be of length k if allowing different component shape parameters, or a single value if fix.alpha = TRUE. If NULL, then the initial value is estimated by partitioning the data into k regions (with lambda determining the proportion of values in each region) and then calculating the method of moments estimates.

beta

Starting value of vector of component scale parameters. If non-NULL and a vector, k is set to length(beta). If NULL, then the initial value is estimated the same method described for alpha.

k

Number of components. Initial value ignored unless alpha and beta are both NULL.

mom.start

Logical to indicate if a method of moments starting value strategy should be implemented. If TRUE, then only unspecified starting values will be generated according to this strategy.

epsilon

The convergence criterion. Convergence is declared when the change in the observed data log-likelihood increases by less than epsilon.

fix.alpha

Logical to indicate if the components should have a common shape parameter alpha estimated. The default is FALSE.

maxit

The maximum number of iterations.

maxrestarts

The maximum number of restarts allowed in case of a problem with the particular starting values chosen (each restart uses randomly chosen starting values).

verb

If TRUE, then various updates are printed during each iteration of the algorithm.

Value

gammamixEM returns a list of class mixEM with items:

x

The raw data.

lambda

The final mixing proportions.

gamma.pars

A 2xk matrix where each column provides the component estimates of alpha and beta.

loglik

The final log-likelihood.

posterior

An nxk matrix of posterior probabilities for observations.

all.loglik

A vector of each iteration's log-likelihood. This vector includes both the initial and the final values; thus, the number of iterations is one less than its length.

ft

A character vector giving the name of the function.

References

Dempster, A. P., Laird, N. M., and Rubin, D. B. (1977) Maximum Likelihood From Incomplete Data Via the EM Algorithm, Journal of the Royal Statistical Society, Series B, 39(1), 1–38.

Young, D. S., Chen, X., Hewage, D., and Nilo-Poyanco, R. (2019) Finite Mixture-of-Gamma Distributions: Estimation, Inference, and Model-Based Clustering, Advances in Data Analysis and Classification, 13(4), 1053–1082.

Examples

##Analyzing a 3-component mixture of gammas.

set.seed(100)
x <- c(rgamma(200, shape = 0.2, scale = 14), rgamma(200, 
     shape = 32, scale = 10), rgamma(200, shape = 5, scale = 6))
out <- gammamixEM(x, lambda = c(1, 1, 1)/3, verb = TRUE)
#> number of iterations= 25 
#> iteration = 1  log-lik diff = 1175.88  log-lik = -2608.276 
#> iteration = 2  log-lik diff = 47.74193  log-lik = -2560.534 
#> iteration = 3  log-lik diff = 10.27375  log-lik = -2550.26 
#> iteration = 4  log-lik diff = 4.378686  log-lik = -2545.881 
#> iteration = 5  log-lik diff = 2.703569  log-lik = -2543.178 
#> iteration = 6  log-lik diff = 2.013168  log-lik = -2541.165 
#> iteration = 7  log-lik diff = 1.657544  log-lik = -2539.507 
#> iteration = 8  log-lik diff = 1.441377  log-lik = -2538.066 
#> iteration = 9  log-lik diff = 1.293605  log-lik = -2536.772 
#> iteration = 10  log-lik diff = 1.183348  log-lik = -2535.589 
#> iteration = 11  log-lik diff = 1.095632  log-lik = -2534.493 
#> iteration = 12  log-lik diff = 1.022566  log-lik = -2533.471 
#> iteration = 13  log-lik diff = 0.9596622  log-lik = -2532.511 
#> iteration = 14  log-lik diff = 0.9043369  log-lik = -2531.607 
#> iteration = 15  log-lik diff = 0.8544442  log-lik = -2530.752 
#> iteration = 16  log-lik diff = 0.8093044  log-lik = -2529.943 
#> iteration = 17  log-lik diff = 0.7679066  log-lik = -2529.175 
#> iteration = 18  log-lik diff = 0.7296704  log-lik = -2528.445 
#> iteration = 19  log-lik diff = 0.6941591  log-lik = -2527.751 
#> iteration = 20  log-lik diff = 0.6610344  log-lik = -2527.09 
#> iteration = 21  log-lik diff = 0.6300273  log-lik = -2526.46 
#> iteration = 22  log-lik diff = 0.6009192  log-lik = -2525.859 
#> iteration = 23  log-lik diff = 0.5735289  log-lik = -2525.286 
#> iteration = 24  log-lik diff = 0.5477037  log-lik = -2524.738 
#> iteration = 25  log-lik diff = 0.523313  log-lik = -2524.215 
#> iteration = 26  log-lik diff = 0.5002437  log-lik = -2523.714 
#> iteration = 27  log-lik diff = 0.4783967  log-lik = -2523.236 
#> iteration = 28  log-lik diff = 0.4576846  log-lik = -2522.778 
#> iteration = 29  log-lik diff = 0.4380291  log-lik = -2522.34 
#> iteration = 30  log-lik diff = 0.4193604  log-lik = -2521.921 
#> iteration = 31  log-lik diff = 0.4015763  log-lik = -2521.519 
#> iteration = 32  log-lik diff = 0.3847644  log-lik = -2521.134 
#> iteration = 33  log-lik diff = 0.3686747  log-lik = -2520.766 
#> iteration = 34  log-lik diff = 0.3533688  log-lik = -2520.412 
#> iteration = 35  log-lik diff = 0.3387888  log-lik = -2520.074 
#> iteration = 36  log-lik diff = 0.3248889  log-lik = -2519.749 
#> iteration = 37  log-lik diff = 0.3116312  log-lik = -2519.437 
#> iteration = 38  log-lik diff = 0.2989803  log-lik = -2519.138 
#> iteration = 39  log-lik diff = 0.2869034  log-lik = -2518.851 
#> iteration = 40  log-lik diff = 0.2753699  log-lik = -2518.576 
#> iteration = 41  log-lik diff = 0.2643513  log-lik = -2518.312 
#> iteration = 42  log-lik diff = 0.2538208  log-lik = -2518.058 
#> iteration = 43  log-lik diff = 0.2437535  log-lik = -2517.814 
#> iteration = 44  log-lik diff = 0.2341259  log-lik = -2517.58 
#> iteration = 45  log-lik diff = 0.224916  log-lik = -2517.355 
#> iteration = 46  log-lik diff = 0.2161031  log-lik = -2517.139 
#> iteration = 47  log-lik diff = 0.2076678  log-lik = -2516.931 
#> iteration = 48  log-lik diff = 0.1995918  log-lik = -2516.732 
#> iteration = 49  log-lik diff = 0.1919381  log-lik = -2516.54 
#> iteration = 50  log-lik diff = 0.184525  log-lik = -2516.355 
#> iteration = 51  log-lik diff = 0.1774225  log-lik = -2516.178 
#> iteration = 52  log-lik diff = 0.1706174  log-lik = -2516.007 
#> iteration = 53  log-lik diff = 0.1641054  log-lik = -2515.843 
#> iteration = 54  log-lik diff = 0.1578627  log-lik = -2515.685 
#> iteration = 55  log-lik diff = 0.1518768  log-lik = -2515.533 
#> iteration = 56  log-lik diff = 0.146136  log-lik = -2515.387 
#> iteration = 57  log-lik diff = 0.1406293  log-lik = -2515.246 
#> iteration = 58  log-lik diff = 0.135346  log-lik = -2515.111 
#> iteration = 59  log-lik diff = 0.1302761  log-lik = -2514.981 
#> iteration = 60  log-lik diff = 0.1254102  log-lik = -2514.855 
#> iteration = 61  log-lik diff = 0.1207392  log-lik = -2514.735 
#> iteration = 62  log-lik diff = 0.1162546  log-lik = -2514.618 
#> iteration = 63  log-lik diff = 0.1119481  log-lik = -2514.506 
#> iteration = 64  log-lik diff = 0.1078121  log-lik = -2514.399 
#> iteration = 65  log-lik diff = 0.1038392  log-lik = -2514.295 
#> iteration = 66  log-lik diff = 0.1000222  log-lik = -2514.195 
#> iteration = 67  log-lik diff = 0.09635467  log-lik = -2514.098 
#> iteration = 68  log-lik diff = 0.09283012  log-lik = -2514.006 
#> iteration = 69  log-lik diff = 0.0894425  log-lik = -2513.916 
#> iteration = 70  log-lik diff = 0.08618604  log-lik = -2513.83 
#> iteration = 71  log-lik diff = 0.08305525  log-lik = -2513.747 
#> iteration = 72  log-lik diff = 0.08004486  log-lik = -2513.667 
#> iteration = 73  log-lik diff = 0.07714987  log-lik = -2513.59 
#> iteration = 74  log-lik diff = 0.07436551  log-lik = -2513.515 
#> iteration = 75  log-lik diff = 0.07168721  log-lik = -2513.444 
#> iteration = 76  log-lik diff = 0.06911063  log-lik = -2513.375 
#> iteration = 77  log-lik diff = 0.06663161  log-lik = -2513.308 
#> iteration = 78  log-lik diff = 0.06424617  log-lik = -2513.244 
#> iteration = 79  log-lik diff = 0.06195054  log-lik = -2513.182 
#> iteration = 80  log-lik diff = 0.05974108  log-lik = -2513.122 
#> iteration = 81  log-lik diff = 0.05761433  log-lik = -2513.064 
#> iteration = 82  log-lik diff = 0.05556697  log-lik = -2513.009 
#> iteration = 83  log-lik diff = 0.05359586  log-lik = -2512.955 
#> iteration = 84  log-lik diff = 0.05169794  log-lik = -2512.904 
#> iteration = 85  log-lik diff = 0.04987033  log-lik = -2512.854 
#> iteration = 86  log-lik diff = 0.04811025  log-lik = -2512.806 
#> iteration = 87  log-lik diff = 0.04641505  log-lik = -2512.759 
#> iteration = 88  log-lik diff = 0.04478219  log-lik = -2512.714 
#> iteration = 89  log-lik diff = 0.04320923  log-lik = -2512.671 
#> iteration = 90  log-lik diff = 0.04169384  log-lik = -2512.629 
#> iteration = 91  log-lik diff = 0.04023379  log-lik = -2512.589 
#> iteration = 92  log-lik diff = 0.03882694  log-lik = -2512.55 
#> iteration = 93  log-lik diff = 0.03747124  log-lik = -2512.513 
#> iteration = 94  log-lik diff = 0.03616473  log-lik = -2512.477 
#> iteration = 95  log-lik diff = 0.03490552  log-lik = -2512.442 
#> iteration = 96  log-lik diff = 0.0336918  log-lik = -2512.408 
#> iteration = 97  log-lik diff = 0.03252185  log-lik = -2512.376 
#> iteration = 98  log-lik diff = 0.031394  log-lik = -2512.344 
#> iteration = 99  log-lik diff = 0.03030666  log-lik = -2512.314 
#> iteration = 100  log-lik diff = 0.0292583  log-lik = -2512.285 
#> iteration = 101  log-lik diff = 0.02824746  log-lik = -2512.256 
#> iteration = 102  log-lik diff = 0.02727271  log-lik = -2512.229 
#> iteration = 103  log-lik diff = 0.02633272  log-lik = -2512.203 
#> iteration = 104  log-lik diff = 0.02542618  log-lik = -2512.177 
#> iteration = 105  log-lik diff = 0.02455186  log-lik = -2512.153 
#> iteration = 106  log-lik diff = 0.02370854  log-lik = -2512.129 
#> iteration = 107  log-lik diff = 0.02289508  log-lik = -2512.106 
#> iteration = 108  log-lik diff = 0.02211038  log-lik = -2512.084 
#> iteration = 109  log-lik diff = 0.02135338  log-lik = -2512.063 
#> iteration = 110  log-lik diff = 0.02062305  log-lik = -2512.042 
#> iteration = 111  log-lik diff = 0.01991842  log-lik = -2512.022 
#> iteration = 112  log-lik diff = 0.01923854  log-lik = -2512.003 
#> iteration = 113  log-lik diff = 0.01858252  log-lik = -2511.984 
#> iteration = 114  log-lik diff = 0.01794947  log-lik = -2511.966 
#> iteration = 115  log-lik diff = 0.01733727  log-lik = -2511.949 
#> iteration = 116  log-lik diff = 0.01674776  log-lik = -2511.932 
#> iteration = 117  log-lik diff = 0.0161788  log-lik = -2511.916 
#> iteration = 118  log-lik diff = 0.01562965  log-lik = -2511.901 
#> iteration = 119  log-lik diff = 0.01509961  log-lik = -2511.885 
#> iteration = 120  log-lik diff = 0.01458799  log-lik = -2511.871 
#> iteration = 121  log-lik diff = 0.01409501  log-lik = -2511.857 
#> iteration = 122  log-lik diff = 0.01361816  log-lik = -2511.843 
#> iteration = 123  log-lik diff = 0.01315782  log-lik = -2511.83 
#> iteration = 124  log-lik diff = 0.0127134  log-lik = -2511.817 
#> iteration = 125  log-lik diff = 0.01228434  log-lik = -2511.805 
#> iteration = 126  log-lik diff = 0.01187007  log-lik = -2511.793 
#> iteration = 127  log-lik diff = 0.01147009  log-lik = -2511.782 
#> iteration = 128  log-lik diff = 0.01108387  log-lik = -2511.771 
#> iteration = 129  log-lik diff = 0.01071093  log-lik = -2511.76 
#> iteration = 130  log-lik diff = 0.0103508  log-lik = -2511.75 
#> iteration = 131  log-lik diff = 0.01000302  log-lik = -2511.739 
#> iteration = 132  log-lik diff = 0.009667163  log-lik = -2511.73 
#> iteration = 133  log-lik diff = 0.009342803  log-lik = -2511.72 
#> iteration = 134  log-lik diff = 0.009029536  log-lik = -2511.711 
#> iteration = 135  log-lik diff = 0.008726973  log-lik = -2511.703 
#> iteration = 136  log-lik diff = 0.008434736  log-lik = -2511.694 
#> iteration = 137  log-lik diff = 0.008152465  log-lik = -2511.686 
#> iteration = 138  log-lik diff = 0.00787981  log-lik = -2511.678 
#> iteration = 139  log-lik diff = 0.007616434  log-lik = -2511.671 
#> iteration = 140  log-lik diff = 0.007362015  log-lik = -2511.663 
#> iteration = 141  log-lik diff = 0.007116239  log-lik = -2511.656 
#> iteration = 142  log-lik diff = 0.006878806  log-lik = -2511.649 
#> iteration = 143  log-lik diff = 0.006649424  log-lik = -2511.643 
#> iteration = 144  log-lik diff = 0.006427816  log-lik = -2511.636 
#> iteration = 145  log-lik diff = 0.006213711  log-lik = -2511.63 
#> iteration = 146  log-lik diff = 0.006006848  log-lik = -2511.624 
#> iteration = 147  log-lik diff = 0.005806978  log-lik = -2511.618 
#> iteration = 148  log-lik diff = 0.005613859  log-lik = -2511.613 
#> iteration = 149  log-lik diff = 0.005427258  log-lik = -2511.607 
#> iteration = 150  log-lik diff = 0.005246949  log-lik = -2511.602 
#> iteration = 151  log-lik diff = 0.005072716  log-lik = -2511.597 
#> iteration = 152  log-lik diff = 0.004904351  log-lik = -2511.592 
#> iteration = 153  log-lik diff = 0.00474165  log-lik = -2511.587 
#> iteration = 154  log-lik diff = 0.004584421  log-lik = -2511.583 
#> iteration = 155  log-lik diff = 0.004432475  log-lik = -2511.578 
#> iteration = 156  log-lik diff = 0.004285631  log-lik = -2511.574 
#> iteration = 157  log-lik diff = 0.004143714  log-lik = -2511.57 
#> iteration = 158  log-lik diff = 0.004006557  log-lik = -2511.566 
#> iteration = 159  log-lik diff = 0.003873996  log-lik = -2511.562 
#> iteration = 160  log-lik diff = 0.003745875  log-lik = -2511.558 
#> iteration = 161  log-lik diff = 0.003622041  log-lik = -2511.554 
#> iteration = 162  log-lik diff = 0.00350235  log-lik = -2511.551 
#> iteration = 163  log-lik diff = 0.003386661  log-lik = -2511.548 
#> iteration = 164  log-lik diff = 0.003274836  log-lik = -2511.544 
#> iteration = 165  log-lik diff = 0.003166745  log-lik = -2511.541 
#> iteration = 166  log-lik diff = 0.003062261  log-lik = -2511.538 
#> iteration = 167  log-lik diff = 0.002961262  log-lik = -2511.535 
#> iteration = 168  log-lik diff = 0.00286363  log-lik = -2511.532 
#> iteration = 169  log-lik diff = 0.00276925  log-lik = -2511.529 
#> iteration = 170  log-lik diff = 0.002678013  log-lik = -2511.527 
#> iteration = 171  log-lik diff = 0.002589812  log-lik = -2511.524 
#> iteration = 172  log-lik diff = 0.002504546  log-lik = -2511.522 
#> iteration = 173  log-lik diff = 0.002422113  log-lik = -2511.519 
#> iteration = 174  log-lik diff = 0.002342421  log-lik = -2511.517 
#> iteration = 175  log-lik diff = 0.002265375  log-lik = -2511.515 
#> iteration = 176  log-lik diff = 0.002190886  log-lik = -2511.513 
#> iteration = 177  log-lik diff = 0.00211887  log-lik = -2511.51 
#> iteration = 178  log-lik diff = 0.002049241  log-lik = -2511.508 
#> iteration = 179  log-lik diff = 0.001981921  log-lik = -2511.506 
#> iteration = 180  log-lik diff = 0.001916832  log-lik = -2511.504 
#> iteration = 181  log-lik diff = 0.001853899  log-lik = -2511.503 
#> iteration = 182  log-lik diff = 0.001793049  log-lik = -2511.501 
#> iteration = 183  log-lik diff = 0.001734213  log-lik = -2511.499 
#> iteration = 184  log-lik diff = 0.001677323  log-lik = -2511.497 
#> iteration = 185  log-lik diff = 0.001622315  log-lik = -2511.496 
#> iteration = 186  log-lik diff = 0.001569124  log-lik = -2511.494 
#> iteration = 187  log-lik diff = 0.001517691  log-lik = -2511.493 
#> iteration = 188  log-lik diff = 0.001467957  log-lik = -2511.491 
#> iteration = 189  log-lik diff = 0.001419864  log-lik = -2511.49 
#> iteration = 190  log-lik diff = 0.001373359  log-lik = -2511.488 
#> iteration = 191  log-lik diff = 0.001328387  log-lik = -2511.487 
#> iteration = 192  log-lik diff = 0.001284899  log-lik = -2511.486 
#> iteration = 193  log-lik diff = 0.001242845  log-lik = -2511.485 
#> iteration = 194  log-lik diff = 0.001202176  log-lik = -2511.483 
#> iteration = 195  log-lik diff = 0.001162847  log-lik = -2511.482 
#> iteration = 196  log-lik diff = 0.001124813  log-lik = -2511.481 
#> iteration = 197  log-lik diff = 0.001088031  log-lik = -2511.48 
#> iteration = 198  log-lik diff = 0.00105246  log-lik = -2511.479 
#> iteration = 199  log-lik diff = 0.001018059  log-lik = -2511.478 
#> iteration = 200  log-lik diff = 0.0009847889  log-lik = -2511.477 
#> iteration = 201  log-lik diff = 0.000952613  log-lik = -2511.476 
#> iteration = 202  log-lik diff = 0.0009214947  log-lik = -2511.475 
#> iteration = 203  log-lik diff = 0.0008913989  log-lik = -2511.474 
#> iteration = 204  log-lik diff = 0.0008622916  log-lik = -2511.473 
#> iteration = 205  log-lik diff = 0.0008341402  log-lik = -2511.472 
#> iteration = 206  log-lik diff = 0.000806913  log-lik = -2511.472 
#> iteration = 207  log-lik diff = 0.0007805794  log-lik = -2511.471 
#> iteration = 208  log-lik diff = 0.0007551099  log-lik = -2511.47 
#> iteration = 209  log-lik diff = 0.0007304758  log-lik = -2511.469 
#> iteration = 210  log-lik diff = 0.0007066495  log-lik = -2511.469 
#> iteration = 211  log-lik diff = 0.0006836043  log-lik = -2511.468 
#> iteration = 212  log-lik diff = 0.0006613145  log-lik = -2511.467 
#> iteration = 213  log-lik diff = 0.0006397551  log-lik = -2511.467 
#> iteration = 214  log-lik diff = 0.000618902  log-lik = -2511.466 
#> iteration = 215  log-lik diff = 0.0005987318  log-lik = -2511.465 
#> iteration = 216  log-lik diff = 0.0005792221  log-lik = -2511.465 
#> iteration = 217  log-lik diff = 0.0005603511  log-lik = -2511.464 
#> iteration = 218  log-lik diff = 0.0005420977  log-lik = -2511.464 
#> iteration = 219  log-lik diff = 0.0005244415  log-lik = -2511.463 
#> iteration = 220  log-lik diff = 0.0005073629  log-lik = -2511.463 
#> iteration = 221  log-lik diff = 0.000490843  log-lik = -2511.462 
#> iteration = 222  log-lik diff = 0.0004748632  log-lik = -2511.462 
#> iteration = 223  log-lik diff = 0.0004594058  log-lik = -2511.461 
#> iteration = 224  log-lik diff = 0.0004444537  log-lik = -2511.461 
#> iteration = 225  log-lik diff = 0.0004299901  log-lik = -2511.46 
#> iteration = 226  log-lik diff = 0.0004159991  log-lik = -2511.46 
#> iteration = 227  log-lik diff = 0.0004024652  log-lik = -2511.46 
#> iteration = 228  log-lik diff = 0.0003893732  log-lik = -2511.459 
#> iteration = 229  log-lik diff = 0.0003767087  log-lik = -2511.459 
#> iteration = 230  log-lik diff = 0.0003644577  log-lik = -2511.459 
#> iteration = 231  log-lik diff = 0.0003526066  log-lik = -2511.458 
#> iteration = 232  log-lik diff = 0.0003411422  log-lik = -2511.458 
#> iteration = 233  log-lik diff = 0.0003300519  log-lik = -2511.457 
#> iteration = 234  log-lik diff = 0.0003193233  log-lik = -2511.457 
#> iteration = 235  log-lik diff = 0.0003089447  log-lik = -2511.457 
#> iteration = 236  log-lik diff = 0.0002989046  log-lik = -2511.457 
#> iteration = 237  log-lik diff = 0.0002891918  log-lik = -2511.456 
#> iteration = 238  log-lik diff = 0.0002797957  log-lik = -2511.456 
#> iteration = 239  log-lik diff = 0.0002707058  log-lik = -2511.456 
#> iteration = 240  log-lik diff = 0.0002619122  log-lik = -2511.455 
#> iteration = 241  log-lik diff = 0.0002534051  log-lik = -2511.455 
#> iteration = 242  log-lik diff = 0.0002451751  log-lik = -2511.455 
#> iteration = 243  log-lik diff = 0.0002372133  log-lik = -2511.455 
#> iteration = 244  log-lik diff = 0.0002295108  log-lik = -2511.454 
#> iteration = 245  log-lik diff = 0.0002220591  log-lik = -2511.454 
#> iteration = 246  log-lik diff = 0.00021485  log-lik = -2511.454 
#> iteration = 247  log-lik diff = 0.0002078756  log-lik = -2511.454 
#> iteration = 248  log-lik diff = 0.0002011283  log-lik = -2511.454 
#> iteration = 249  log-lik diff = 0.0001946005  log-lik = -2511.453 
#> iteration = 250  log-lik diff = 0.0001882852  log-lik = -2511.453 
#> iteration = 251  log-lik diff = 0.0001821754  log-lik = -2511.453 
#> iteration = 252  log-lik diff = 0.0001762643  log-lik = -2511.453 
#> iteration = 253  log-lik diff = 0.0001705455  log-lik = -2511.453 
#> iteration = 254  log-lik diff = 0.0001650127  log-lik = -2511.453 
#> iteration = 255  log-lik diff = 0.0001596599  log-lik = -2511.452 
#> iteration = 256  log-lik diff = 0.0001544811  log-lik = -2511.452 
#> iteration = 257  log-lik diff = 0.0001494707  log-lik = -2511.452 
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#> iteration = 523  log-lik diff = 2.233082e-08  log-lik = -2511.448 
#> iteration = 524  log-lik diff = 2.157594e-08  log-lik = -2511.448 
#> iteration = 525  log-lik diff = 2.084471e-08  log-lik = -2511.448 
#> iteration = 526  log-lik diff = 2.01394e-08  log-lik = -2511.448 
#> iteration = 527  log-lik diff = 1.945591e-08  log-lik = -2511.448 
#> iteration = 528  log-lik diff = 1.879516e-08  log-lik = -2511.448 
#> iteration = 529  log-lik diff = 1.815715e-08  log-lik = -2511.448 
#> iteration = 530  log-lik diff = 1.753961e-08  log-lik = -2511.448 
#> iteration = 531  log-lik diff = 1.694252e-08  log-lik = -2511.448 
#> iteration = 532  log-lik diff = 1.636499e-08  log-lik = -2511.448 
#> iteration = 533  log-lik diff = 1.580656e-08  log-lik = -2511.448 
#> iteration = 534  log-lik diff = 1.526678e-08  log-lik = -2511.448 
#> iteration = 535  log-lik diff = 1.474518e-08  log-lik = -2511.448 
#> iteration = 536  log-lik diff = 1.423996e-08  log-lik = -2511.448 
#> iteration = 537  log-lik diff = 1.375292e-08  log-lik = -2511.448 
#> iteration = 538  log-lik diff = 1.328044e-08  log-lik = -2511.448 
#> iteration = 539  log-lik diff = 1.282433e-08  log-lik = -2511.448 
#> iteration = 540  log-lik diff = 1.238413e-08  log-lik = -2511.448 
#> iteration = 541  log-lik diff = 1.195713e-08  log-lik = -2511.448 
#> iteration = 542  log-lik diff = 1.154513e-08  log-lik = -2511.448 
#> iteration = 543  log-lik diff = 1.114677e-08  log-lik = -2511.448 
#> iteration = 544  log-lik diff = 1.07616e-08  log-lik = -2511.448 
#> iteration = 545  log-lik diff = 1.038916e-08  log-lik = -2511.448 
#> iteration = 546  log-lik diff = 1.002945e-08  log-lik = -2511.448 
#> iteration = 547  log-lik diff = 9.681571e-09  log-lik = -2511.448 
#> number of iterations= 547 
out[2:4]
#> $lambda
#> [1] 0.3215866 0.3450800 0.3333333
#> 
#> $gamma.pars
#>          comp.1   comp.2   comp.3
#> alpha 0.2109625 5.144978 30.55456
#> beta  8.9941068 5.766442 10.68708
#> 
#> $loglik
#> [1] -2511.448
#>