School of Mathematics, Statistics and Actuarial Sciences
https://repository.maseno.ac.ke/handle/123456789/92
Thu, 27 Jan 2022 11:22:48 GMT2022-01-27T11:22:48ZOn some properties of generalized Fibonacci polynomials
https://repository.maseno.ac.ke/handle/123456789/4686
On some properties of generalized Fibonacci polynomials
Fidel Oduol
Fibonacci polynomials have been generalized mainly by two ways: by maintaining the recurrence
relation and varying the initial conditions and by varying the recurrence relation and maintaining the
initial conditions. In this paper, both the recurrence relation and initial conditions of generalized Fibonacci
polynomials are varied and defined by recurrence relation as Rn(x) = axRn−1(x) + bRn−2(x) for all n ≥ 2,
with initial conditions R0(x) = 2p and R1(x) = px + q where a and b are positive integers and p and q
are non-negative integers. Further some fundamental properties of these generalized polynomials such as
explicit sum formula, sum of first n terms, sum of first n terms with (odd or even) indices and generalized
identity are derived by Binet’s formula and generating function only
Wed, 01 Jan 2020 00:00:00 GMThttps://repository.maseno.ac.ke/handle/123456789/46862020-01-01T00:00:00ZModels for Level Premiums Payable to Benevolent Funds
https://repository.maseno.ac.ke/handle/123456789/4644
Models for Level Premiums Payable to Benevolent Funds
Chora Damary Rehema, Fredrick Onyango, Joshua Were
The application of multiple life actuarial calculations have been stud ied by many authours for instance Elizondo [3] studied the construction
of multiple decrement models from associated single decrement expe riences.He posits that it is convenient to use the survival functions for
the projection of future obligations in cash flows. Bowers [2] studied the
actuarial calculations which are common in estate and gift taxation.The
actuarial calculation is also common in insurance where stipulated pay ment called the benefit, one party (the insurer) agrees to pay to the
other (the policyholder or his designated beneficiary) a defined amount
(the claim payment or benefit) upon the occurrence of a specific loss
while the insured pays periodic payment called premium. SACCOs and
institution provide benevolent in terms of insurance against some losses,
especially death. Unfortunately such organizations determine their pre miums arbitrarily, thus one cannot tell whether such products are de generating or not,this is because in such bodies benevolent funds and
the mainstream operation fund are usually confounded.In this paper we
develop models for level premiums for Saccos and Institutions provid ing benevolent funds, that is premiums is independent on the number
of beneficiaries.We will use models of joint life,last life and multiple
decrements to develop this model.
Wed, 01 Jan 2020 00:00:00 GMThttps://repository.maseno.ac.ke/handle/123456789/46442020-01-01T00:00:00ZOn Generalized Fibonacci Numbers
https://repository.maseno.ac.ke/handle/123456789/4625
On Generalized Fibonacci Numbers
Fidel Ochieng Oduol, Isaac Owino Okoth
Fibonacci numbers and their polynomials have been generalized mainly by two ways: by maintaining the
recurrence relation and varying the initial conditions, and by varying the recurrence relation and maintaining the
initial conditions. In this paper, we introduce and derive various properties of r-sum Fibonacci numbers. The
recurrence relation is maintained but initial conditions are varied. Among results obtained are Binet’s formula,
generating function, explicit sum formula, sum of first n terms, sum of first n terms with even indices, sum of
first n terms with odd indices, alternating sum of n terms of r−sum Fibonacci sequence, Honsberger’s identity,
determinant identities and a generalized identity from which Cassini’s identity, Catalan’s identity and d’Ocagne’s
identity follow immediately
Wed, 01 Jan 2020 00:00:00 GMThttps://repository.maseno.ac.ke/handle/123456789/46252020-01-01T00:00:00ZRefined enumeration of 2-noncrossing trees
https://repository.maseno.ac.ke/handle/123456789/4624
Refined enumeration of 2-noncrossing trees
Isaac Owino Okoth
A 2-noncrossing tree is a connected graph without cycles that can be drawn in the
plane with its vertices on the boundary of circle such that the edges are straight line segments that
do not cross and all the vertices are coloured black and white with no ascent (i, j), where i and j
are black vertices, in a path from the root. In this paper, we use generating functions to prove a
formula that counts 2-noncrossing trees with a black root to take into account the number of white
vertices of indegree greater than zero and black vertices. Here, the edges of the 2-noncrossing
trees are oriented from a vertex of lower label towards a vertex of higher label. The formula is
a refinement of the formula for the number of 2-noncrossing trees that was obtained by Yan and
Liu and later on generalized by Pang and Lv. As a consequence of the refinement, we find an
equivalent refinement for 2-noncrossing trees with a white root, among other results
Fri, 01 Jan 2021 00:00:00 GMThttps://repository.maseno.ac.ke/handle/123456789/46242021-01-01T00:00:00Z