On Order Statistics for GS-Distributions

In this article, a class of distributions is used to establish several recurrence relations satisfied by single and product moments of order statistics and progressive Type-II right censoring. The recurrence relations for moments of some specific distributions including uniform (a;b); exponential (λ); generalized exponential (α;λ;ν); beta (1;b); beta (b;1); logistic (α;β) and other distributions from order statistics and progressive Type-II right censoring can be obtained as special cases. A short explanation of GS-distribution can be found in reference [27]. As an example, means, variances and covariances for standard exponential distribution of progressive Type-II right censored order statistics are computed. Various characterizations of the recently introduced GS-distributions are presented. These characterizations are based on a simple relationship between two truncated moments ; on hazard function ; and on functions of order statistics. A characterization of the GS-distributions based on conditional moment of order statistics is extended to truncated moment of order statistics

Simultaneous determination of sulpiride and mebeverine by HPLC method using fluorescence detection: application to real human plasma

A new simple, rapid and sensitive reversed-phase liquid chromatographic method was developed and validated for the simultaneous determination of sulpiride (SUL) and mebeverine Hydrochloride (MEB) in the presence of their impurities and degradation products. The separation of these compounds was achieved within 6 min on a 250 mm, 4.6 mm i.d., 5 m particle size Waters®-C18 column using isocractic mobile phase containing a mixture of acetonitrile and 0.01 M dihydrogenphosphate buffer (45:55) at pH = 4.0. The analysis was performed at a flow rate of 1.0 mL/min with fluorescence-detection at excitation 300 nm and emission at 365 nm. The concentration-response relationship was linear over a concentration range of 10- 100 ng/mL for both MEB and SUL with a limit of detection 0.73 ng/mL and 0.85 ng/mL for MEB and SUL respectively. The proposed method was successfully applied for the analysis of both MEB and SUL in bulk with average recoveries of 100.22 ± 0.757% and 99.96 ± 0.625% respectively, and in commercial tablets with average recoveries of 100.04 ± 0.93% and 100.03 ± 0.376% for MEB and SUL respectively. The proposed method was successfully applied to the determination of MEB metabolite (veratic acid) in real plasma simultaneously with SUL. The mean% recoveries (n = 3) for both MEB metabolite (veratic acid) and SUL were 100.36 ± 2.92 and 99.06 ± 2.11 for spiked human plasma respectively. For real human plasma, the mean% recoveries (n = 3) were and respectively

Estimation in Step-Stress Accelerated Life Tests for Weibull Distribution with Progressive First-Failure Censoring

Abstract: Based on progressive first-failure censoring, step-stress partially accelerated life tests are considered when the lifetime of a product follows Weibull distribution. The maximum likelihood estimates (MLEs) are obtained for the distribution parameters and the acceleration factor. In addition, asymptotic variance and covariance matrix of the estimators are given. Furthermore, confidence intervals of the estimators are presented. The optimal stress change time for the step-stress partially accelerated life test is determined by minimizing the asymptotic variance of MLEs of the model parameters and the acceleration factor. Simulation results are carried out to study the precision of the MLEs for the parameters involved

Statistical inference for the Nadarajah-Haghighi distribution based on ranked set sampling with applications

In this article, the maximum likelihood and Bayes inference methods are discussed for determining the two unknown parameters and specific lifetime parameters of the Nadarajah-Haghighi distribution, such as the survival and hazard rate functions, with the inclusion of ranked set sampling and simple random sampling. The estimated confidence intervals for the two parameters and any function of them are developed based on the Fisher-information matrix. Metropolis-Hastings algorithm and Lindley-approximation are used for generating the Bayes estimates and related highest posterior density credible ranges for the unknown parameters and reliability parameters under the presumption of conjugate gamma priors. A Monte-Carlo simulation study and a real-life data set have been used to assess the efficacy of the proposed methods

Validated stability indicating liquid chromatographic determination of ebastine in pharmaceuticals after pre column derivatization: Application to tablets and content uniformity testing

An accurate, simple, sensitive and selective reversed phase liquid chromatographic method has been developed for the determination of ebastine in its pharmaceutical preparations. The proposed method depends on the complexation ability of the studied drug with Zn2+ ions. Reversed phase chromatography was conducted using an ODS C18 (150 × 4.6 mm id) stainless steel column at ambient temperature with UV-detection at 260 nm. A mobile phase containing 0.025%w/v Zn2+ in a mixture of (acetonitril/methanol; 1/4) and Britton Robinson buffer (65:35, v/v) adjusted to pH 4.2, has been used for the determination of ebastine at a flow rate of 1 ml/min. The calibration curve was rectilinear over the concentration range of 0.3 - 6.0 μg/ml with a detection limit (LOD) of 0.13 μg/ml, and quantification limit (LOQ) of 0.26 μg/ml. The proposed method was successfully applied for the analysis of ebastine in its dosage forms, the obtained results were favorably compared with those obtained by a comparison method. Furthermore, content uniformity testing of the studied pharmaceutical formulations was also conducted. The composition of the complex as well as its stability constant was also investigated. Moreover, the proposed method was found to be a stability indicating one and was utilized to investigate the kinetics of alkaline and ultraviolet induced degradation of the drug. The first-order rate constant and half life of the degradation products were calculated

Validated stability-indicating spectrofluorimetric methods for the determination of ebastine in pharmaceutical preparations

Two sensitive, selective, economic, and validated spectrofluorimetric methods were developed for the determination of ebastine (EBS) in pharmaceutical preparations depending on reaction with its tertiary amino group. Method I involves condensation of the drug with mixed anhydrides (citric and acetic anhydrides) producing a product with intense fluorescence, which was measured at 496 nm after excitation at 388 nm

Characterization of the generalized Pareto distribution by general progressively Type-II right censored order statistics

In this article, we establish recurrence relations for single and product moments based on general progressively Type-II right censored order statistics (GPTIICOS). Characterization for generalized Pareto distribution (GPD) using relation between probability density function and distribution function and using recurrence relations of single and product moments of GPTIICOS are also obtained. Further, the results are specialized to the progressively Type-II right censored order statistics (PTIICOS) and specialized to the Pareto, uniform and exponential distributions. Keywords: Characterization, Generalizeneralized Pareto distribution, General progressively Type-II right censored order statistics, Recurrence relations, Single and product moment

Bayesian Estimation and Two-sample Prediction Based on Unified Hybrid Censored Sample

In this paper, a general inverse exponential form of the underlying distribution and a general conjugate prior are used to discuss the maximum likelihood and Bayesian estimation based on unified hybrid censored sample. A general procedure for deriving two-sample Bayesian prediction is developed using unified hybrid censoring scheme. Special cases of the inverse Weibull model such as the inverse exponential and the inverse Rayleigh distributions are then used as illustrative examples. Finally, numerical examples are presented for illustrating all the inferential procedures developed here

Prediction of Generalized Order Statistics Based on Some Accelerated Data Using the Tampered Failure Rate Model

Prediction of generalized order sample can be done with normal bounds having suitable confidence. However, given independent samples from the same absolutely continuous distribution, the prediction based on some accelerated bounds can be achieved. In this regard, this paper deals some various exact non-parametric prediction intervals for the future generalized order statistics under normal operating conditions based on stressed generalized order variables were observed in step stress accelerated life test: The tampered failure rate model. The progressive Type-II right-censoring order sample of failure time data that presented by Xiong [1] are used in numerical computations to illustrate the proposed procedures