Two new goodness-of-fit testing procedures are introduced to test exponentiality when data are su... more Two new goodness-of-fit testing procedures are introduced to test exponentiality when data are subject to Type-I censoring. We proposed four test statistics for this purpose. Under extensive Monte Carlo simulations, we showed that the proposed tests maintain the nominal significance level and show good power for both monotonic and non-monotonic hazard function alternatives even for small samples as n = 10. A real dataset is studied for illustrative purposes.
In this article, we propose two goodness-of-fit test statistics for the Burr Type X distribution ... more In this article, we propose two goodness-of-fit test statistics for the Burr Type X distribution when the available data are subject to progressively Type-II censoring. The proposed test statistics are based on the sample correlation coefficient between the Kaplan-Meier estimator of the survival function and the lifetime data and also based on the correlation between the Nelson-Aalen estimator of the cumulative hazard function and the lifetime data. The new tests exhibit good performance in terms of power in compare to the EDF-based test statistics of Pakyari and Balakrishnan (IEEE Trans Reliab 61:238-242, 2012). The maximum likelihood estimator of the unknown Burr Type X model is also studied and an approximate estimator is given. Finally, two real datasets are analyzed for illustrative purposes.
Two bagging approaches, say \(\frac{1}{2}n\)-out-of-\(n\) without replacement (subagging) and \(n... more Two bagging approaches, say \(\frac{1}{2}n\)-out-of-\(n\) without replacement (subagging) and \(n\)-out-of-\(n\) with replacement (bagging) have been applied in the problem of estimation of the parameters in a multivariate mixture model. It has been observed by Monte Carlo simulations and a real data example, that both bagging methods have improved the standard deviation of the maximum likelihood estimator of the mixing proportion, whilst the absolute bias increased slightly. In estimating the component distributions, bagging could increase the root mean integrated squared error when estimating the most probable component.
Background: The failure time of permanent tooth is of the form of interval censored since the exa... more Background: The failure time of permanent tooth is of the form of interval censored since the exact time of tooth decay is not available and it is only known that tooth decay occurs between two consecutive visits. There are a few techniques available in the literature for the problem of goodnessof-fit for interval censored data. In this paper, we propose a new goodness-of-fit testing procedure for interval censored data and employ this for the failure time of the first permanent molar tooth (sixth tooth) data. Materials and Methods: Two methods of goodness-of-fit for interval censored data that are based on randomly generated data from each interval and averaging over the test statistics or over the p-values are employed for the failure time of the first permanent molar tooth data. Results: The mean of the failure time of the first permanent molar tooth is found to be at 95 months. The p-values of the two goodness-of-fit testing procedures for the Weibull, log-normal and gamma model...
Geometric Extreme Exponential Distribution (GEE) is one of the statistical models that can be use... more Geometric Extreme Exponential Distribution (GEE) is one of the statistical models that can be useful in fitting and describing lifetime data. In this paper, the problem of estimation of the reliability R = P(Y < X) when X and Y are independent GEE random variables with common scale parameter but different shape parameters has been considered. The probability R = P(Y < X) is also known as stress-strength reliability parameter and demonstrates the case where a component has stress X and is subjected to strength Y. The reliability R = P(Y < X) has applications in engineering, finance and biomedical sciences. We present the maximum likelihood estimator of R and study its asymptotic behavior. We first study the asymptotic distribution of the maximum likelihood estimators of the GEE parameters. We prove that the maximum likelihood estimators and so the reliability R have asymptotic normal distribution. A bootstrap confidence interval for R is also presented. Monte Carlo simulatio...
OBJECTIVE We used sodium nitroprusside (SNP), a nitric oxide (NO) releasing molecule, to understa... more OBJECTIVE We used sodium nitroprusside (SNP), a nitric oxide (NO) releasing molecule, to understand its effect on viability and proliferation of rat bone marrow mesenchymal stem cells (BM-MSCs). MATERIALS AND METHODS This experimental study evaluated the viability and morphology of MSCs in the presence of SNP (100 to 2000 µM) at 1, 5, and 15 hours. We chose the 100, 1000, and 2000 µM concentrations of SNP for one hour exposure for further analyses. Cell proliferation was investigated by the colony forming assay and population doubling number (PDN). Na+, K+, and Ca2+ levels as well as activities of lactate dehydrogenase (LDH), alkaline phosphatase (ALP), aspartate transaminase (AST), and alanine transaminase (ALT) were measured. RESULTS The viability of MSCs dose-dependently reduced from 750 µM at one hour and 250 µM at 5 and 15 hours. The 100 µM caused no change in viability, however we observed a reduction in the cytoplasmic area at 5 and 15 hours. This change was not observed at o...
Survival comparison is one of the main goals and interesting problems in most survival studies su... more Survival comparison is one of the main goals and interesting problems in most survival studies such as clinical studies. In this paper, we compare through a Monte Carlo study, several tests for comparison of survival functions for interval censored failure time data. In particular, three nonparametric generalized log-rank tests, a parametric score test and an imputation-based test have been considered. It is observed that the parametric score test and the imputation test outperform the nonparametric generalized log-rank tests in most cases. Finally, a real dataset is studied for illustrative purposes.
Communications in Statistics - Simulation and Computation, 2021
In this article, we propose two new scale invariant test statistics when the available data are s... more In this article, we propose two new scale invariant test statistics when the available data are subject to progressively Type-II censoring. The proposed tests are based on Gini index of spacings. It is observed thorough extensive Monte Carlo simulations that the proposed tests are quite powerful in compare to similar existing goodness-of-fit tests studied by Balakrishnan et al. and Wang. We also illustrate the method proposed here using a real data from reliability literature.
We propose an extension of Kullback-Leibler information to the survival function, and generalize ... more We propose an extension of Kullback-Leibler information to the survival function, and generalize it to the censored case. We evaluate its performance as a goodness-of-fit test statistic with the progressively Type-II censored data. The new test is evaluated through Monte Carlo Simulations.
Communications in Statistics - Simulation and Computation, 2016
ABSTRACT A goodness-of-fit test procedure is proposed for some lifetime distributions when the av... more ABSTRACT A goodness-of-fit test procedure is proposed for some lifetime distributions when the available data are subject to Type-I censoring. The proposed method extends the test procedure of Pakyari and Balakrishnan to other lifetime distributions. The extension to Weibull and log-normal models is studied in details. The new test recovers the nominal level of significance and exhibits more power in comparison to the existing tests for several alternative distributions by means of Monte Carlo simulations. Finally, a real dataset is considered for illustrative purposes.
Geometric extreme exponential (GE-exponential) is one of the nonnegative right-skewed distributio... more Geometric extreme exponential (GE-exponential) is one of the nonnegative right-skewed distribution that is suitable for analyzing lifetime data. It is well known that the maximum likelihood estimators (MLEs) of the parameters lead to likelihood equations that have to be solved numerically. In this paper, we provide explicit estimators through an approximation of the likelihood equations based on progressively Type-II-censored samples. The approximate estimators are then used as starting values to find the MLEs numerically. The bias and variances of the MLEs are calculated for a wide range of sample sizes and different progressive censoring schemes through a Monte Carlo simulation study. Moreover, formulas for the observed Fisher information are given which could be used to construct asymptotic confidence intervals. The coverage probabilities of the confidence intervals and the percentage points of pivotal quantities associated with the MLEs are also calculated. A real dataset has be...
Journal of Statistical Computation and Simulation, 2013
The problem of goodness-of-fit for the exponential distribution when the available data are subje... more The problem of goodness-of-fit for the exponential distribution when the available data are subject to Type-I censoring is discussed here. A test procedure is proposed in this case that exhibits more power as compared to existing methods. The power of the proposed test is assessed for several alternative distributions by means of Monte Carlo simulations. Finally, the proposed test is illustrated with a real data set.
Journal of Statistical Computation and Simulation, 2009
HERE -Generalized exponential, geometric extreme exponential and Weibull distributions are three ... more HERE -Generalized exponential, geometric extreme exponential and Weibull distributions are three nonnegative skewed distributions that are suitable for analyzing lifetime data. We present diagnostic tools based on the likelihood ratio test (LRT) and the minimum Kolmogorov distance (KD) method to discriminate between these models. Probability of correct selection (PCS) has been calculated for each model and for several combinations of shape parameters and sample sizes using Monte Carlo simulation.
Communications in Statistics - Theory and Methods, 2009
The asymptotic behavior of the nonparametric density estimator has been given for a multivariate ... more The asymptotic behavior of the nonparametric density estimator has been given for a multivariate mixture model. It has been observed that the estimator is asymptotically normally distributed with bias of size h and variance of size (nh).
... B PETER HALL, AMNON NEEMAN, REZA PAKYARI RYAN ELMORE Centre for Mathematics and its Appl... more ... B PETER HALL, AMNON NEEMAN, REZA PAKYARI RYAN ELMORE Centre for Mathematics and its Applications, Australian National University, Canberra, ACT 0200, Australiapeter.hall@maths.anu.edu.auamnon.neeman@maths.anu.edu.au reza ... 2), Titterington et al. ...
Two new goodness-of-fit testing procedures are introduced to test exponentiality when data are su... more Two new goodness-of-fit testing procedures are introduced to test exponentiality when data are subject to Type-I censoring. We proposed four test statistics for this purpose. Under extensive Monte Carlo simulations, we showed that the proposed tests maintain the nominal significance level and show good power for both monotonic and non-monotonic hazard function alternatives even for small samples as n = 10. A real dataset is studied for illustrative purposes.
In this article, we propose two goodness-of-fit test statistics for the Burr Type X distribution ... more In this article, we propose two goodness-of-fit test statistics for the Burr Type X distribution when the available data are subject to progressively Type-II censoring. The proposed test statistics are based on the sample correlation coefficient between the Kaplan-Meier estimator of the survival function and the lifetime data and also based on the correlation between the Nelson-Aalen estimator of the cumulative hazard function and the lifetime data. The new tests exhibit good performance in terms of power in compare to the EDF-based test statistics of Pakyari and Balakrishnan (IEEE Trans Reliab 61:238-242, 2012). The maximum likelihood estimator of the unknown Burr Type X model is also studied and an approximate estimator is given. Finally, two real datasets are analyzed for illustrative purposes.
Two bagging approaches, say \(\frac{1}{2}n\)-out-of-\(n\) without replacement (subagging) and \(n... more Two bagging approaches, say \(\frac{1}{2}n\)-out-of-\(n\) without replacement (subagging) and \(n\)-out-of-\(n\) with replacement (bagging) have been applied in the problem of estimation of the parameters in a multivariate mixture model. It has been observed by Monte Carlo simulations and a real data example, that both bagging methods have improved the standard deviation of the maximum likelihood estimator of the mixing proportion, whilst the absolute bias increased slightly. In estimating the component distributions, bagging could increase the root mean integrated squared error when estimating the most probable component.
Background: The failure time of permanent tooth is of the form of interval censored since the exa... more Background: The failure time of permanent tooth is of the form of interval censored since the exact time of tooth decay is not available and it is only known that tooth decay occurs between two consecutive visits. There are a few techniques available in the literature for the problem of goodnessof-fit for interval censored data. In this paper, we propose a new goodness-of-fit testing procedure for interval censored data and employ this for the failure time of the first permanent molar tooth (sixth tooth) data. Materials and Methods: Two methods of goodness-of-fit for interval censored data that are based on randomly generated data from each interval and averaging over the test statistics or over the p-values are employed for the failure time of the first permanent molar tooth data. Results: The mean of the failure time of the first permanent molar tooth is found to be at 95 months. The p-values of the two goodness-of-fit testing procedures for the Weibull, log-normal and gamma model...
Geometric Extreme Exponential Distribution (GEE) is one of the statistical models that can be use... more Geometric Extreme Exponential Distribution (GEE) is one of the statistical models that can be useful in fitting and describing lifetime data. In this paper, the problem of estimation of the reliability R = P(Y < X) when X and Y are independent GEE random variables with common scale parameter but different shape parameters has been considered. The probability R = P(Y < X) is also known as stress-strength reliability parameter and demonstrates the case where a component has stress X and is subjected to strength Y. The reliability R = P(Y < X) has applications in engineering, finance and biomedical sciences. We present the maximum likelihood estimator of R and study its asymptotic behavior. We first study the asymptotic distribution of the maximum likelihood estimators of the GEE parameters. We prove that the maximum likelihood estimators and so the reliability R have asymptotic normal distribution. A bootstrap confidence interval for R is also presented. Monte Carlo simulatio...
OBJECTIVE We used sodium nitroprusside (SNP), a nitric oxide (NO) releasing molecule, to understa... more OBJECTIVE We used sodium nitroprusside (SNP), a nitric oxide (NO) releasing molecule, to understand its effect on viability and proliferation of rat bone marrow mesenchymal stem cells (BM-MSCs). MATERIALS AND METHODS This experimental study evaluated the viability and morphology of MSCs in the presence of SNP (100 to 2000 µM) at 1, 5, and 15 hours. We chose the 100, 1000, and 2000 µM concentrations of SNP for one hour exposure for further analyses. Cell proliferation was investigated by the colony forming assay and population doubling number (PDN). Na+, K+, and Ca2+ levels as well as activities of lactate dehydrogenase (LDH), alkaline phosphatase (ALP), aspartate transaminase (AST), and alanine transaminase (ALT) were measured. RESULTS The viability of MSCs dose-dependently reduced from 750 µM at one hour and 250 µM at 5 and 15 hours. The 100 µM caused no change in viability, however we observed a reduction in the cytoplasmic area at 5 and 15 hours. This change was not observed at o...
Survival comparison is one of the main goals and interesting problems in most survival studies su... more Survival comparison is one of the main goals and interesting problems in most survival studies such as clinical studies. In this paper, we compare through a Monte Carlo study, several tests for comparison of survival functions for interval censored failure time data. In particular, three nonparametric generalized log-rank tests, a parametric score test and an imputation-based test have been considered. It is observed that the parametric score test and the imputation test outperform the nonparametric generalized log-rank tests in most cases. Finally, a real dataset is studied for illustrative purposes.
Communications in Statistics - Simulation and Computation, 2021
In this article, we propose two new scale invariant test statistics when the available data are s... more In this article, we propose two new scale invariant test statistics when the available data are subject to progressively Type-II censoring. The proposed tests are based on Gini index of spacings. It is observed thorough extensive Monte Carlo simulations that the proposed tests are quite powerful in compare to similar existing goodness-of-fit tests studied by Balakrishnan et al. and Wang. We also illustrate the method proposed here using a real data from reliability literature.
We propose an extension of Kullback-Leibler information to the survival function, and generalize ... more We propose an extension of Kullback-Leibler information to the survival function, and generalize it to the censored case. We evaluate its performance as a goodness-of-fit test statistic with the progressively Type-II censored data. The new test is evaluated through Monte Carlo Simulations.
Communications in Statistics - Simulation and Computation, 2016
ABSTRACT A goodness-of-fit test procedure is proposed for some lifetime distributions when the av... more ABSTRACT A goodness-of-fit test procedure is proposed for some lifetime distributions when the available data are subject to Type-I censoring. The proposed method extends the test procedure of Pakyari and Balakrishnan to other lifetime distributions. The extension to Weibull and log-normal models is studied in details. The new test recovers the nominal level of significance and exhibits more power in comparison to the existing tests for several alternative distributions by means of Monte Carlo simulations. Finally, a real dataset is considered for illustrative purposes.
Geometric extreme exponential (GE-exponential) is one of the nonnegative right-skewed distributio... more Geometric extreme exponential (GE-exponential) is one of the nonnegative right-skewed distribution that is suitable for analyzing lifetime data. It is well known that the maximum likelihood estimators (MLEs) of the parameters lead to likelihood equations that have to be solved numerically. In this paper, we provide explicit estimators through an approximation of the likelihood equations based on progressively Type-II-censored samples. The approximate estimators are then used as starting values to find the MLEs numerically. The bias and variances of the MLEs are calculated for a wide range of sample sizes and different progressive censoring schemes through a Monte Carlo simulation study. Moreover, formulas for the observed Fisher information are given which could be used to construct asymptotic confidence intervals. The coverage probabilities of the confidence intervals and the percentage points of pivotal quantities associated with the MLEs are also calculated. A real dataset has be...
Journal of Statistical Computation and Simulation, 2013
The problem of goodness-of-fit for the exponential distribution when the available data are subje... more The problem of goodness-of-fit for the exponential distribution when the available data are subject to Type-I censoring is discussed here. A test procedure is proposed in this case that exhibits more power as compared to existing methods. The power of the proposed test is assessed for several alternative distributions by means of Monte Carlo simulations. Finally, the proposed test is illustrated with a real data set.
Journal of Statistical Computation and Simulation, 2009
HERE -Generalized exponential, geometric extreme exponential and Weibull distributions are three ... more HERE -Generalized exponential, geometric extreme exponential and Weibull distributions are three nonnegative skewed distributions that are suitable for analyzing lifetime data. We present diagnostic tools based on the likelihood ratio test (LRT) and the minimum Kolmogorov distance (KD) method to discriminate between these models. Probability of correct selection (PCS) has been calculated for each model and for several combinations of shape parameters and sample sizes using Monte Carlo simulation.
Communications in Statistics - Theory and Methods, 2009
The asymptotic behavior of the nonparametric density estimator has been given for a multivariate ... more The asymptotic behavior of the nonparametric density estimator has been given for a multivariate mixture model. It has been observed that the estimator is asymptotically normally distributed with bias of size h and variance of size (nh).
... B PETER HALL, AMNON NEEMAN, REZA PAKYARI RYAN ELMORE Centre for Mathematics and its Appl... more ... B PETER HALL, AMNON NEEMAN, REZA PAKYARI RYAN ELMORE Centre for Mathematics and its Applications, Australian National University, Canberra, ACT 0200, Australiapeter.hall@maths.anu.edu.auamnon.neeman@maths.anu.edu.au reza ... 2), Titterington et al. ...
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Papers by Reza Pakyari