External Analysis of Strategic Market Management Can Be Realized Based upon Different Human Mindset – a Debate in the Light of Statistical Perspective

The paper entails the statistical correlation of the investigations carried out for the sales and profit prediction and analysis by persons of different mindsets in case of strategic uncertainty. The paper by virtue of statistical and fuzzy logic based justifications has pointed out certain discovered facts in this perspective. The normal , optimistic , pessimistic and fickle-minded based individual mindsets significantly contribute to varying external analysis of business statistics.


INTRODUCTION
Strategic development or review [1] deals with an analysis of the factors external to a business that affect strategy.In strategic market management, estimation of sales and profit plays a significant role .Sometimes a separate statistical analyst team is solely recruited in certain business companies.A running business can be investigated on the basis of apriori events and statistical trend analysis [2,3].However in certain cases due to some external stochastic events, statistical analysis has to be carried out based upon prediction and forecasting and in this perspective of strategic uncertainty , the business estimate varies from individual to individual depending on his nature viz.normal , optimistic , pessimistic and fickle-minded.

II. VARIATION OF EXTERNAL ANALYSIS OF STRATEGIC MARKET MANAGEMENT BASED ON HUMAN MINDSET
Certain discovered facts can be pointed out pertaining to the variation of external analysis of strategic market management depending on the human nature.We propose certain mathematically established axioms in this context.An opportunity or a threat results in a significant change in pattern of the sales and profit of a business.Marketing Myopia [4] also indicates the essence of investigation of sales and profit in case of strategic uncertainty.Furthermore, profit and loss are two mutually exclusive events at any specific timing instant of the observation period.Therefore, R , the Bernoulli random variable [5] for the external analysis of business strategy in this situation , can be viewed as - R is a statistical indicator of X or Y.
Claim 1 -If prediction of occurrence of gain in a strategic market management by a normal individual is based upon estimation of weight of single associated parameter and hypothesis of fairness by pessimistic individual is rejected , then for unit negative bias, the estimate of weight of the single parameter by either historical or predictive means by a normal person is represented as a complex variable.

Illustration of Claim 1 -
In case of business uncertainty, predictive decisions among various business analysts differ considerably.A normal person will efficiently judge the current status of the business and try to predict in a concise manner.
In many cases it can be observed that optimistic , pessimistic and fickle minded persons predict the sales and profit status defying the current status and hence the statistical hypothesis as per their predictions are likely to be biased.
In this claim, we propose the correlation of estimation of normal person with a pessimistic individual.The proposed mathematical equation of neuro-fuzzy based www.ijarai.thesai.orgevent (gain) estimation between a pessimistic and a normal individual in case of strategic uncertainty is as followsx Tp + β = AWn = [ ( ∑ AW x,i * AW y,i ) / x ] …………….. (1) i=1 where Tp = average accuracy estimation of gain by pessimistic individual, β = unit negative bias value AWn = effective weight of the associated parameters per prediction by a normal individual AW x,i = estimate of weight of i th parameter on the basis of sampled historical information , AW y,i = estimate of weight of i th parameter on the basis of present hypothesis, x = total number of instances of the arrival of the event gain As per our proposal , single incidence of gain takes place and hypothesis of fairness by pessimistic individual is rejected .
Therefore, AW x,1 * AW y,1 = 0 + β or, (AW y,1 ) 2 = β or, (AW y,1 ) 2 = -1 [ since unit negative bias ] or, AW y,1 = (-1 ) 1/2 ………………….…………….…….( 2) Similarly, we can show that AW x,1 = (-1 ) 1/2 ………..... (3) Hence it is justified to state that "If prediction of occurrence of gain by a normal individual is based upon estimate of weight of single parameter and hypothesis of fairness by pessimistic individual is rejected , then for unit negative bias, the estimate of weight of the single parameter by either historical or predictive means by a normal person is represented as a complex variable".Claim 2 -Accuracy estimate of future prediction of occurrence of an uncertain event ( gain or loss ) is governed by the principle of hypothesis of fairness rule in case of both optimistic and pessimistic individuals.

Illustration of Claim 2 -
Strategic uncertainties focus on specific unknown parameters that will affect the outcome of strategic decisions.In this claim we have proposed that the principle of hypothesis rule plays a pivotal role in strategic decisions.A statistical hypothesis [6] is an assertion about the distribution of one or more random variables which we want to verify on the basis of a sample.
In this claim we represent mathematically the relation among predictive gain estimates done by normal , optimistic and pessimistic individuals.
where βo = predicted value of percentage of gain by optimistic person in higher crisp form αn = predicted value percentage of gain by normal person being 0.5 βp = predicted value percentage of gain by pessimistic person in higher crisp form µ = estimate of deviation of both optimistic and pessimistic from actual outcome V ; V € { 0,1 }.
) is valid and it reveals that prediction of optimistic individual is accurate and we reject hypothesis of fairness of pessimistic individual as P ( | 0.5-0 | ≥ (1-0) ) is absurd.
Hence it is justified to state that "Accuracy estimate of future prediction of occurrence of an uncertain event ( gain or loss ) is governed by the principle of hypothesis of fairness rule in case of both optimistic and pessimistic individuals".Claim 3 -In case of sales and profit estimation of strategic market management done by a fickle-minded person , the predicted value (Tv) clearly acts as a reference parameter for identifying the output (To) trends towards both rare and frequent fuzzy domains.

Illustration of Claim 3 -
Fuzzy set theory was proposed in 1965 by Lotfi A. Zadeh.A fuzzy set [7] can be defined mathematically by assigning to each possible individual in the universe of discourse, a value representing its grade of membership in the fuzzy set.
In definite form , crisp value is coined and it is in bivalent or binary variable state {0,1}, while the fuzzy value is in probabilistic form and lower and higher crisps indicate the lower and upper boundary limits of a fuzzy range.The average (0.5) is a threshold that indicates rare range (0 L R 0.5 ) and frequent range ( 0.5 F R 1 ).
The following table illustrates that in case of the sales and profit estimation of strategic market management done by a fickle-minded person, the predicted value (Tv) clearly acts as a reference parameter for identifying the output (To) trends towards both rare fuzzy (L R ) and frequent fuzzy domains (F R ).C L and C H represent lower and higher crisp values respectively.

Table 1 : Gain estimation depending on different human mindset and
Hence it is justified to state that "In case of sales and profit estimation of strategic market management done by a fickleminded person , the predicted value (Tv) clearly acts as a reference parameter for identifying the output (To) trends towards both rare and frequent fuzzy domains".Claim 4 -The null hypothesis of validity of an unknown event ( gain or loss ) for a biased individual is identical to alternate hypothesis of the same for a normal person.

Illustration of Claim 4 -
In this claim we have proposed that in case of strategic uncertainty, the general statistical rules of null and alternated hypothesis can be significantly correlated with the external analysis of strategic market management in the view of a biased ( either optimistic or pessimistic) and normal person.Let p be unknown binary state of validity of an event ( gain or loss) in case of biased individual and q s is specific fuzzy estimate.
Therefore, H 0 : p = q s ……………………………………..... (5) and H A : p ≠ q s ……………………………………….(6) where H 0 and H A are null and alternate hypothesis respectively of biased person.In this context biased person indicates optimistic and pessimistic nature of a person.Now, (1-p) is unknown binary state of validity of an event ( gain or loss) in case of normal person and q n be specific fuzzy estimate.
Since the event is valid, hence q s = q n =1 .
Biased property reflects false belief which means Eq(5) is invalid.In that case the validity of Eq(6) concludes that p ≠ q s .Now q s has to be in higher crisp whereby p = 0.
Let us examine whether Eq( 7) is valid under this circumstance.
For Eq (7) to be valid , (1-p) = q n = 1.Now q n has to be 1 whereby p = 0.It indicates that alternate hypothesis of schizophrenic patient is identical to the null hypothesis of normal person, and vice-versa.
Hence it is justified to state that "The null hypothesis of validity of an unknown event ( gain or loss ) for a biased individual is identical to alternate hypothesis of the same for a normal person."

III. CONCLUSION
The paper points out the following discovered facts -1.If prediction of occurrence of gain in a strategic market management by a normal individual is based upon estimation of weight of single associated parameter and hypothesis of fairness by pessimistic individual is rejected , then for unit negative bias, the estimate of weight of the single parameter by either historical or predictive means by a normal person is represented as a complex variable.
2. Accuracy estimate of future prediction of occurrence of an uncertain event ( gain or loss ) is governed by the principle of hypothesis of fairness rule in case of both optimistic and pessimistic individuals.
3. In case of sales and profit estimation of strategic market management done by a fickle-minded person , the predicted value (Tv) clearly acts as a reference parameter for identifying the output (To) trends towards both rare and frequent fuzzy domains.
4. The null hypothesis of validity of an unknown event ( gain or loss ) for a biased individual is identical to alternate hypothesis of the same for a normal person.