Survival Analysis: Techniques for Censored and Truncated Data (2nd ed.) (Book)

An Introduction to Probability Theory and its Applications, Volume I

Continuous Univariate Distributions Volume 2

(k, l) [1885]. (n− k + 1) [1753, 1623]. 0 [772]. 0 < ρ < ρ0 [2026]. 1 [772, 548]. $109.95 [2218]. $125.00 [2161]. $129.95 [2259]. 1 ≤ p <∞ [562]. 2 [616, 407]. $229.00 [2019]. 24 [1398]. 24 [1476]. 2s−k [2039]. 3 [852, 2125]. $49.95 [2161]. $59.95 [2219]. $89.95 [2217]. (R) [2002, 1962]. 1 [1276]. 2 [1417]. k [798]. A [1577, 2312, 2346]. α [858, 1840, 2242, 1465, 1271, 1945, 2327, 1926]. AR(1) [1650, 790]. AR(p) [1346]. R̄ [652]. β [668, 856, 497]. c [2332]. χ [919]. D [2135, 2268, 836, 948, 1324, 2309, 2346, 2098, 2176]. δ [1959]. e [596]. E(x⊗ xx′) [1805]. E(xx′ ⊗ xx′) [1805]. F [1901, 915, 1361, 407, 681]. G [548]. Γ [722]. H [1664]. I(1) [845]. K [2308, 1551, 1223, 1837, 368, 479, 2177, 1322, 1198, 2224, 2309, 407, 1932]. k − 2 [1781]. L [439, 1974, 1584, 1399, 1322]. L1 [895]. L2 [2195, 2363, 2039]. LP [562]. LM [1343]. LR [1343]. M [1054, 1107, 2094, 2180]. Lp [1552]. N [816, 752, 48, 1753, 1623, 548]. p [1245, 1461, 2378, 1794, 1868, 1604, 1791, 1589, 2074, 2227]. P (X < Y ) [1867, 1492, 1955]. P (Y < X) [2222, 1380]. Φ [1345]. Pr(a < x < b) [263]. q [1651]. R [1238, 1848, 616, 1932]. r − k [2082, 1480]. R/S [1996]. R = Pr(X > Y ) [2007]. r [1446]. ρ∗ [1884]. S [2151, 1105]. S [848, 790, 909]. σ [1141, 684]. SUNn,2 [2046]. t [1054, 1777, 327, 1533, 1722, 982, 856, 1031, 1780, 1559, 1094, 1391, 1342, 1680]. T 2

/pdf/a-complete-bibliography-of-publications-in-statistical-u76lky1hh4.pdf

A Complete Bibliography of Publications in Statistical Papers

The progressive Type-II hybrid censoring scheme introduced by Kundu and Joarder (Comput Stat Data Anal 50:2509–2528, 2006), has received some attention in the last few years. One major drawback of this censoring scheme is that very few observations (even no observation at all) may be observed at the end of the experiment. To overcome this problem, Cho et al. (Stat Methodol 23:18–34, 2015) recently introduced generalized progressive censoring which ensures to get a pre specified number of failures. In this paper we analyze generalized progressive censored data in presence of competing risks. For brevity we have considered only two competing causes of failures, and it is assumed that the lifetime of the competing causes follow one parameter exponential distributions with different scale parameters. We obtain the maximum likelihood estimators of the unknown parameters and also provide their exact distributions. Based on the exact distributions of the maximum likelihood estimators exact confidence intervals can be obtained. Asymptotic and bootstrap confidence intervals are also provided for comparison purposes. We further consider the Bayesian analysis of the unknown parameters under a very flexible beta–gamma prior. We provide the Bayes estimates and the associated credible intervals of the unknown parameters based on the above priors. We present extensive simulation results to see the effectiveness of the proposed method and finally one real data set is analyzed for illustrative purpose.

On generalized progressive hybrid censoring in presence of competing risks

Exact likelihood inference for exponential distributions under generalized progressive hybrid censoring schemes

In this paper, a structural analysis of hybrid censoring models is presented. This new modularization approach to hybrid censoring models enables a convenient derivation of distributional results. For instance, it allows to derive the exact distribution of the MLEs under an exponential assumption for very complex hybrid scenarios. In order to illustrate the benefit of this idea, we apply it to four new unified progressive hybrid censoring schemes. They are extensions of already proposed unified Type-I/II/III/IV hybrid censoring schemes to progressively Type-II censored data. The resulting analysis shows that the modularization approach provides a powerful, efficient, and elegant tool to study even more complex hybrid censoring models.

Modularization of hybrid censoring schemes and its application to unified progressive hybrid censoring

Type-I censored sequential k-out-of-n systems

Distributions of the maximum likelihood estimators (MLEs) in Type-II (progressive) hybrid censoring based on two-parameter exponential distributions have been obtained using a moment generating function approach. Although resulting in explicit expressions, the representations are complicated alternating sums. Using the spacings-based approach of Cramer and Balakrishnan [On some exact distributional results based on Type-I progressively hybrid censored data from exponential distributions. Statist Methodol. 2013;10:128–150], we derive simple expressions for the exact density and distribution functions of the MLEs in terms of B-spline functions. These representations can be easily implemented on a computer and provide an efficient method to compute density and distribution functions as well as moments of Type-II (progressively) hybrid censored order statistics.

On the exact distribution of the MLEs based on Type-II progressively hybrid censored data from exponential distributions

We establish an identity that relates B-spline functions to linear combinations of gamma density functions. Utilizing this connection, we illustrate that, for exponentially distributed lifetimes, the distribution of the MLE in various hybrid censoring schemes can be expressed in terms of gamma density functions with simple weights. As an example, representations for the density functions in the case of Type-I sequential, Type-II progressive hybrid, generalized Type-I progressive hybrid, and generalized Type-II progressive hybrid censoring schemes are presented. It turns out that the representations arising from the spacings’ based approach introduced in Cramer and Balakrishnan (Stat Methodol 10:128–150, 2013) are more compact than those available in the literature so far.

Julian Górny

Papers

Exact likelihood inference for exponential distributions under generalized progressive hybrid censoring schemes

Modularization of hybrid censoring schemes and its application to unified progressive hybrid censoring

Type-I censored sequential k-out-of-n systems

On the exact distribution of the MLEs based on Type-II progressively hybrid censored data from exponential distributions

From B-spline representations to gamma representations in hybrid censoring