Some Methods of Estimation from Censored Samples in Exponential and Gamma Models

Two popular life testing models exponential and one where its generalization is gamma are considered. Estimation of scale parameter from a general Type-II doubly censored sample is attempted by the principle of maximum likelihood method. Resulting equations found to be giving iterative solutions. As an alternative to iterative solution certain admissible modifications to the estimating equations are suggested in special cases. The resulting estimates are compared with the exact maximum likelihood estimates analytically or through simulation. The results are also extended for reliability estimation

Discriminating Between Generalized Exponential Distribution and Some Life Test Models Based on Population Quantiles

A test statistic based on population quantiles using sample order statistics is suggested. The quantiles of the test statistics are evaluated for generalized exponential distribution. Similar test statistic based on moments of sample order statistic is referred and the proposed test formula is compared with it. Between the pairs of the above models it is established that the test formula proposed by us is more effective and useful than the formula based on the moments of order statistics as developed by Sultan (2007)

Limited Failure Censored Life Test Sampling Plan in Burr Type X Distribution

The Burr type X distribution is considered as a life time random variable of a product whose lots are to be decided for acceptance or otherwise on the basis of sample lifetimes drawn from the lot. The sample is divided into various groups in order to develop a group sampling plan in such a way that the life testing experiment is terminated as soon as the first failure in each group is observed. The acceptance criterion based on the theory of order statistics is proposed and is shown to be more economical than a criterion proposed in the earlier similar works

Estimation and Testing in Type I Generalized Half Logistic Distribution

A generalization of the half logistic distribution is developed through exponentiation of its cumulative distribution function and termed the Type I Generalized Half Logistic Distribution (GHLD). GHLD’s distributional characteristics and parameter estimation using maximum likelihood and modified maximum likelihood methods are presented with comparisons. Comparison of Type I GHLD and the exponential distribution is conducted via likelihood ratio criterion

Likelihood Ratio Type Test for Linear Failure Rate Distribution vs. Exponential Distribution

The Linear Failure Rate Distribution (LFRD) is considered. The graphs of its probability density function are examined for selected parameter combinations. Some of them are similar to the well-known exponential distribution. Incidentally exponential distribution is one of the two component models of the LFRD model. In view of the simpler form of exponential model as applicable in inference, looking at the frequency curves of LFRD, a test statistic is proposed based on ratio of likelihood functions containing the standard forms of the density functions of both LFRD and Exponential to discriminate between LFRD and exponential models. The critical values and the powers of the test statistic are developed

Hydrogen-transfer catalysis with Cp*Ir^III complexes:The influence of the ancillary ligands

Fourteen Cp*IrIII complexes, bearing various combinations of N- and C-spectator ligands, are assayed in hydrogen-transfer catalysis from isopropyl alcohol to acetophenone under various conditions to investigate ligand effects in this widely used reaction. The new cationic complexes bearing monodentate pyridine and N-heterocyclic carbene (NHC) ligands were characterized crystallographically and by variable-temperature nuclear magnetic resonance (VT-NMR). Control experiments and mercury poisoning tests showed that iridium(0) nanoparticles, although active in the reaction, are not responsible for the high activity observed for the most active precatalyst [Cp*Ir(IMe) 2Cl]BF4 (6). For efficient catalysis, it was found necessary to have both NHCs in monodentate form; tying them together in a bis-NHC chelate ligand gave greatly reduced activity. The kinetics of the base-assisted reaction showed induction periods as well as deactivation processes, and H/D scrambling experiments cast some doubt on the classical monohydride mechanism. © 2013 American Chemical Society

Structural and functional insights into asymmetric enzymatic dehydration of alkenols

The asymmetric dehydration of alcohols is an important process for the direct synthesis of alkenes. We report the structure and substrate specificity of the bifunctional linalool dehydratase isomerase (LinD) from the bacterium Castellaniella defragrans that catalyzes in nature the hydration of β-myrcene to linalool and the subsequent isomerization to geraniol. Enzymatic kinetic resolutions of truncated and elongated aromatic and aliphatic tertiary alcohols (C5-C15) that contain a specific signature motif demonstrate the broad substrate specificity of LinD. The three-dimensional structure of LinD from Castellaniella defragrans revealed a pentamer with active sites at the protomer interfaces. Furthermore, the structure of LinD in complex with the product geraniol provides initial mechanistic insights into this bifunctional enzyme. Site-directed mutagenesis confirmed active site amino acid residues essential for its dehydration and isomerization activity. These structural and mechanistic insights facilitate the development of hydrating catalysts, enriching the toolbox for novel bond-forming biocatalysis

Variable Control Charts - Linear Failure Rate Distribution

The well known Linear Failure Rate Distribution (LFRD) is considered. A process variate following LFRD is thought of in order to develop control charts for subgroup mean and subgroup range. In view of the limitations on LFRD the theoretical control limits are obtained through some approximations and the resulting control chart limits are worked out. Comparisons with the control limits of similar variable control charts is also presented