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Papers by Kamal Nain

Research paper thumbnail of Recurrence Relations for Single and Product Moments of k th Record Values from Generalized Weibull Distribution and a Characterization

In this paper we established some recurrence relations satisfied by the single and the product mo... more In this paper we established some recurrence relations satisfied by the single and the product moments of k th upper record values from Generalized Weibull distribution. Using a recurrence relation for a single moment, we obtain characterization of Generalized Weibull distribution.

Research paper thumbnail of Recurrence Relations for Single and Product Moments of Ordinary Order Statistics from p th order Exponential Distribution

In this paper, we established some recurrence relations satisfied by single and product moments o... more In this paper, we established some recurrence relations satisfied by single and product moments of ordinary order statistics from p th order exponential distribution. The similar results are also obtained for doubly truncated distribution For a particular case these results are verified from the papers of Balakrishnan and Malik(1986b) and Mohie EI-Din et al. (1997).

Research paper thumbnail of Male and female meiosis evince differential patterns in chiasma formation: a case study of ornamental plant, Delphinium ajacis L

Journal of Genetics, 2020

Chromosomal behaviour during megasporogenesis and microsporogenesis has been studied in ornamenta... more Chromosomal behaviour during megasporogenesis and microsporogenesis has been studied in ornamental Delphinium ajacis L. Meiosis in female sex cell initiates later than male. The floral buds which carry egg mother cell (EMC) at diplotene stage has pollen mother cells (PMCs) at tetrad stage of meiosis suggesting protandry. Although the 16 chromosomes formed regular eight bivalents in both the sex cells, they differed in overall chiasma frequency which was 32.95% higher in EMCs and found to be 18.52 ± 2.12 per cell. In PMCs, the average chiasma frequency recorded was 13.93 ± 1.40 per cell. Interestingly, this variation in chiasma frequency was largely confined to the two large bivalents which shared 42.61% chiasma per EMC. The use of Q–Q plot, Box plot and Whisker plot showed departure in the chiasma frequency distributions in EMCs and PMCs from the normal distribution pattern. The difference in chiasma frequency in the two sex cells was significant at all levels as indicated by the low P values of 3.094 × 10−11 obtained from nonparametric test, i.e. Wilcoxon rank-sum test. It is suggested that the two different mechanisms of recombination are operational in the two sex cells, and the sex differences of chiasma frequency could have arisen due to differential epigenetic modifications of the chromatin which pattern the double-strand breaks, and the position and frequency of crossing over visible as chiasmata.

Research paper thumbnail of Combinatorial approach to M/M/1 queues using hypergeometric functions

International Mathematical Forum, 2013

In this paper we use a well known reflection principle for lattice path counting to apply for the... more In this paper we use a well known reflection principle for lattice path counting to apply for the analysis of the M/M/1 queuing system. The joint distribution of i arrivals and j departures over a time interval of length t is obtained, when there are k customers in the beginning of the system. The derivation uses the lattice path approach between two points, in two dimensional x-y plane with certain restrictions. Finally a known result of queue length is verified from Satty (1961).

Research paper thumbnail of Recurrence Relations for Marginal and Joint Moment Generating Functions of Generalized Order Statistics from a New Class of Pareto Distributions

Journal of Statistical Theory and Applications, 2016

Research paper thumbnail of Relationship between coefficients of characteristic equation

Research paper thumbnail of A new class of cyclic orthogonal designs

Research paper thumbnail of Relationships for moments of k th record values from doubly truncated p th order exponential and generalized Weibull distributions

In this paper we establish some recurrence relations satisfied by the single and the product mome... more In this paper we establish some recurrence relations satisfied by the single and the product moments of k th upper record values from doubly truncated p th order exponential and generalized Weibull distributions.

Research paper thumbnail of Recurrence Relations for Single and Product Moments of k th Record Values from Generalized Weibull Distribution and a Characterization

In this paper we established some recurrence relations satisfied by the single and the product mo... more In this paper we established some recurrence relations satisfied by the single and the product moments of k th upper record values from Generalized Weibull distribution. Using a recurrence relation for a single moment, we obtain characterization of Generalized Weibull distribution.

Research paper thumbnail of Recurrence Relations for Single and Product Moments of Ordinary Order Statistics from p th order Exponential Distribution

In this paper, we established some recurrence relations satisfied by single and product moments o... more In this paper, we established some recurrence relations satisfied by single and product moments of ordinary order statistics from p th order exponential distribution. The similar results are also obtained for doubly truncated distribution For a particular case these results are verified from the papers of Balakrishnan and Malik(1986b) and Mohie EI-Din et al. (1997).

Research paper thumbnail of Male and female meiosis evince differential patterns in chiasma formation: a case study of ornamental plant, Delphinium ajacis L

Journal of Genetics, 2020

Chromosomal behaviour during megasporogenesis and microsporogenesis has been studied in ornamenta... more Chromosomal behaviour during megasporogenesis and microsporogenesis has been studied in ornamental Delphinium ajacis L. Meiosis in female sex cell initiates later than male. The floral buds which carry egg mother cell (EMC) at diplotene stage has pollen mother cells (PMCs) at tetrad stage of meiosis suggesting protandry. Although the 16 chromosomes formed regular eight bivalents in both the sex cells, they differed in overall chiasma frequency which was 32.95% higher in EMCs and found to be 18.52 ± 2.12 per cell. In PMCs, the average chiasma frequency recorded was 13.93 ± 1.40 per cell. Interestingly, this variation in chiasma frequency was largely confined to the two large bivalents which shared 42.61% chiasma per EMC. The use of Q–Q plot, Box plot and Whisker plot showed departure in the chiasma frequency distributions in EMCs and PMCs from the normal distribution pattern. The difference in chiasma frequency in the two sex cells was significant at all levels as indicated by the low P values of 3.094 × 10−11 obtained from nonparametric test, i.e. Wilcoxon rank-sum test. It is suggested that the two different mechanisms of recombination are operational in the two sex cells, and the sex differences of chiasma frequency could have arisen due to differential epigenetic modifications of the chromatin which pattern the double-strand breaks, and the position and frequency of crossing over visible as chiasmata.

Research paper thumbnail of Combinatorial approach to M/M/1 queues using hypergeometric functions

International Mathematical Forum, 2013

In this paper we use a well known reflection principle for lattice path counting to apply for the... more In this paper we use a well known reflection principle for lattice path counting to apply for the analysis of the M/M/1 queuing system. The joint distribution of i arrivals and j departures over a time interval of length t is obtained, when there are k customers in the beginning of the system. The derivation uses the lattice path approach between two points, in two dimensional x-y plane with certain restrictions. Finally a known result of queue length is verified from Satty (1961).

Research paper thumbnail of Recurrence Relations for Marginal and Joint Moment Generating Functions of Generalized Order Statistics from a New Class of Pareto Distributions

Journal of Statistical Theory and Applications, 2016

Research paper thumbnail of Relationship between coefficients of characteristic equation

Research paper thumbnail of A new class of cyclic orthogonal designs

Research paper thumbnail of Relationships for moments of k th record values from doubly truncated p th order exponential and generalized Weibull distributions

In this paper we establish some recurrence relations satisfied by the single and the product mome... more In this paper we establish some recurrence relations satisfied by the single and the product moments of k th upper record values from doubly truncated p th order exponential and generalized Weibull distributions.

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