| Title: | Finite Mixture Model Fitting of Lifespan Datasets |
| Version: | 0.1.0 |
| Description: | Fits the lifespan datasets of biological systems such as yeast, fruit flies, and other similar biological units with well-known finite mixture models introduced by Farewell V. (1982) <doi:10.2307/2529885> and Al-Hussaini et al. (2000) <doi:10.1080/00949650008812033>. Estimates parameter space fitting of a lifespan dataset with finite mixtures of parametric distributions. Computes the following tasks; 1) Estimates parameter space of the finite mixture model by implementing the expectation maximization (EM) algorithm. 2) Finds a sequence of four goodness-of-fit measures consist of Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Kolmogorov-Smirnov (KS), and log-likelihood (log-likelihood) statistics. 3)The initial values is determined by k-means clustering. |
| URL: | https://github.com/guven-code/fitmix/ |
| License: | GPL-3 |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.1.1.9001 |
| Depends: | R (≥ 3.1.0) |
| Imports: | stats |
| Suggests: | rmarkdown, knitr |
| NeedsCompilation: | no |
| Packaged: | 2021-04-17 09:44:53 UTC; user |
| Author: | Emine Guven  [aut,
cre],
Hong Qin [aut] |
| Maintainer: | Emine Guven <emine.guven33@gmail.com> |
| Repository: | CRAN |
| Date/Publication: | 2021-04-19 08:50:04 UTC |
The mixture distribution
Description
Computing probability density function for the well-known mixture models.
Usage
dmix(lifespan, model, K, param)
Arguments
lifespan |
Vector of samples |
model |
choice of one of the mixture models; |
K |
number of components |
param |
Vector of weight |
Value
A vector of the same length as lifespan data, given the pdf of the one of the mixture models computed at lifespan.
Examples
lifespan<-seq(0,30,0.2)
K<-2
weight<-c(0.6,0.4)
alpha<-c(0.5,1)
beta<-c(1,0.5)
param<-c(weight,alpha,beta)
dmix(lifespan, "log-logistic", K, param)
Fits lifespan data of time units with gompertz, log-logistics, log-normal, and weibull mixture models choice of one.
Description
Fits lifespan data of time units with gompertz, log-logistics, log-normal, and weibull mixture models choice of one.
Usage
fitmixEM(lifespan, model, K, initial = FALSE, starts)
Arguments
lifespan |
numeric vector of lifespan dataset |
model |
model name of the one of the well-known model: |
K |
number of well-known model components. |
initial |
logical true or false |
starts |
numeric if initial sets to true |
Details
Estimates parameters of the given mixture model implementing the expectation maximization (EM) algorithm.
General form for the cdf of a statistical mixture model is given by
a distribution f is a mixture of K component distributions of
f = (f_1, f_2,..f_K) if
f(x) = \sum_{k=1}^{K}\lambda_k f_k(x)
with
\lambda_k > 0, \sum_k \lambda_k = 1. This equation is a stochastic model, thus
it allows to generate new data points; first picks a distribution of choice, with
probablities by weight, then generates another observation according to the chosen distribution.
In short represenated by,
Z ~ Mult(\lambda_1, \lambda_2,...\lambda_k) and
X|Z ~ f_Z, where Z is a discrete random variable which component X is drawn from.
The families considered for the cdf of Gompertz, Log-normal, Log-logistic, and Weibull.
Value
1.The return has three values; the first value is estimate, measures, and cluster.
2. The second value includes four different measurements of goodness-of-fit tests involving:
Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Kolmogorov-Smirnov (KS), and log-likelihood (log.likelihood) statistics.
3. The last value is the output of clustering vector.
References
Farewell, V. (1982). The Use of Mixture Models for the Analysis of Survival Data with Long-Term Survivors. Biometrics, 38(4), 1041-1046. doi:10.2307/2529885 McLachlan, G. J. and Peel, D. (2000) Finite Mixture Models, John Wiley \& Sons, Inc.
Essam K. Al-Hussaini, Gannat R. Al-Dayian & Samia A. Adham (2000) On finite mixture of two-component gompertz lifetime model, Journal of Statistical Computation and Simulation, 67:1, 20-67, DOI: 10.1080/00949650008812033
Examples
lifespan<-sample(1000)
fitmixEM(lifespan, "weibull", K = 2, initial = FALSE)
The mixture cumulative distribution
Description
Computing cumulative distribution function for the well-known mixture models.
Usage
pmix(lifespan, model, K, param)
Arguments
lifespan |
Vector of samples |
model |
choice of one of the mixture models; |
K |
number of components |
param |
Vector of weight |
Value
A vector of the same length as lifespan data, given the cdf of the one of the mixture models computed at lifespan.
Examples
lifespan<-seq(0,30,0.2)
K<-2
weight<-c(0.5,0.5)
alpha<-c(0.5,1)
beta<-c(1,0.5)
param<-c(weight,alpha,beta)
pmix(lifespan, "log-logistic", K, param)
The mixture random generation for the well-known models
Description
Random generation for the well-known mixture models with parameters weigth, shape and scale.
Usage
rmix(N, model, K, param)
Arguments
N |
Number of inputs for the mixture random generation |
model |
Choice of one of the mixture models; |
K |
Number of components |
param |
Vector of weight |
Value
Outputs of random generated vector lenght of N from the given mixture model.
Examples
N<-100
K<-2
weight<-c(0.5,0.5)
alpha<-c(0.5,1)
beta<-c(1,0.5)
param<-c(weight,alpha,beta)
rmix(N, "weibull", K, param)